hardware problem

If you are able to boot into Internet Recovery Mode using Command + Option + R, then you should be able to boot into the online Apple Diagnostics since the online diagnostics leverages the same framework as Internet Recovery Mode. If you are unable to boot into Internet Recovery Mode, then you won't be able to boot into the online Apple Diagnostics.

What version of macOS are you running? If you are not running macOS 10.15, then you can try upgrading to a newer major version of macOS which would also upgrade the system firmware. If you are running macOS 10.15 and it is fully patched, then there is probably nothing you can do since Apple has broken the online diagnostics for some users. You can try a PRAM Reset and rebooting your router (allow your router five minutes to finish rebooting) plus try connecting the Mac directly to the router using an Ethernet cable to eliminate any hard to troubleshoot WiFi issues.

Most likely the failure is just a compatibility issue between the system firmware and the online diagnostics and/or Apple servers. You can try creating a bootable USB diagnostic using the files and instructions on this page (the diagnostic file downloads within this article are all from official Apple servers -- just hover over the link to see the URL where the domain portion of the URL is "apple.com"). If your Mac is using the newer style firmware, then even this method will most likely fail due to the same compatibility issue.

https://github.com/upekkha/AppleHardwareTest

Since the Apple Diagnostics are probably not going to work, can you describe in detail the problems you are having with your Mac where you need to run the diagnostics? We may be able to provide some suggestions in troubleshooting your Mac, but we would need some specific details including the exact model of your Mac and version of macOS. It is usually best to run EtreCheck and post the report here using the "Additional Text" icon which looks like a piece of paper. If you give EtreCheck "Full Disk Access", then a summary of the recent logs is also included in the report which may contain additional clues. The EtreCheck report is a quick & easy way of providing contributors lots of useful details about your Mac so we don't have to spend lots of time playing twenty questions for the basic stuff.

Disconnecting all external devices is a good way to make sure that an external device is not the source of the problem.

Your Mac, issued before June of 2013 does not support Internet recovery diagnostics at all, so the error message is not surprising.

the original Apple hardware test was placed in a system directory on your original Boot drive, as well as on disc 2 of the software release disc set 9if so equipped). But if your original boot drive was EVER erased or replaced, no software is responsible for putting the diagnostic back into the system Directories.

https://github.com/upekkha/AppleHardwareTest

provides method for making a BOOTABLE USB-stick diagnostic -- this does NOT work inside MacOS or Internet recovery, it is stand-alone bootable ONLY and will not work any other way than booting DIRECTLY from a properly made and properly blessed USB-stick.

So far you appear to be working very hard to get diagnostics to run on your older computer., which does NOT support the methods you are pursuing.

What is the original symptom that led you down this path?

Those messages are telling you that Apple Diagnostics, loaded over the Internet, are not supported. On late 2012 MacBook Pro, Apple Hardware Test was used.

Apple hardware test has never worked reliably (if at all) from Internet Recovery.

This is not an indication of failure. This is an indication that what you are making for is incompatible.

Grant Bennet-Alder wrote:

Your Mac, issued before June of 2013 does not support Internet recovery diagnostics at all, so the error message is not surprising.

A 2012 MBPro does support Internet Recovery Mode if macOS 10.12.6+ (maybe even 10.12.4) was ever installed on it since it included a system firmware update to allow for the online diagnostics and Internet Recovery Mode. I had a MBPro 2010 that can do both Internet Recovery and the online Apple Diagnostics after one of the 10.12.x updates which pushed new system firmware. The error message displayed by the OP is one I've seen for various reasons over the years. With a couple of the system firmware updates, Apple actually broke some EFI boot files and never bothered to fix some of them. I've never had time to document which firmware updates work and don't work for Internet Recovery Mode and online Apple Diagnostics. It may even be something like how some Macs will refuse to boot into anything but the oldest version of macOS which originally shipped with the Mac from the factory instead of the most recently supported macOS for a particular system.

As shipped from the factory, 2012 and earlier computers did not have access to Internet Recovery Mode or the online Apple Diagnostics.

the original Apple hardware test was placed in a system directory on your original Boot drive, as well as on disc 2 of the software release disc set 9if so equipped). But if your original boot drive was EVER erased or replaced, no software is responsible for putting the diagnostic back into the system Directories.

https://github.com/upekkha/AppleHardwareTest

provides method for making a BOOTABLE USB-stick diagnostic -- this does NOT work inside MacOS or Internet recovery, it is stand-alone bootable ONLY and will not work any other way than booting DIRECTLY from a properly made and properly blessed USB-stick.

Again, the bootable USB diagnostic may not work depending on the system firmware. I've used this to boot one MBPro, but another identical one refused to boot it. It is the same issue I mentioned previously about compatibility issues with some firmware versions and some EFI bootloaders.

ahmedteemo wrote:

i changed only the hard disk and the ram from 4 to 16 . is it the reason for this???

i am a DJ and i just bought this laptop for backup for my work if my main mac have any problem i have another to use so i want to be sure that it has no problem so my work dont stop, thats why i did the hardware test and this error appears

You can use DriveDx to check the health of a hard drive and sometimes an SSD although DriveDx and similar apps don't always interpret the health of an SSD correctly (usually a false failure since these apps sometimes interpret the SSD health reports as if they were hard drives which is not always an accurate interpretation - so use these types of apps with caution regarding SSDs).

You can use a bootable MemTest86 USB stick to check the memory. You can use the downloaded MemTest86 .iso or .img file as a source for Etcher in order to create the bootable MemTest86 USB stick.

Running "mprime" (aka Prime95) in Torture Test Mode will push your computer to its limits so it is a good way to test system stability including the memory, CPU, power, cooling system, etc. This is the same app PC builders and overclockers use to make sure their custom PCs are stable.

To test the GPU, you can run a Unigine Benchmark Demo (only a couple are available for macOS).

I've found a lot of methods like this over the years to test hardware. Sometimes even playing several HD videos can reveal a GPU issue.

As @Grant mentioned only a failing diagnostic or test is actually useful or informative.

Macs issued before June 2013 use Apple Hardware Test, later Macs can use Apple Diagnostics.