Welcome!
If this is the Mid 2012 13-inch NON-Retina Macbook Pro with an optical drive slot, going from 4 to 8GB RAM may help but I can almost guarantee you will NOT see a detectable speed increase. Most "slow "reports for that model are not RAM-related but rather due to the under-spec mechanical hard drives Apple opted to install.
If:
1) the computer is slow to boot up. and...
2) ...big Apps ( like Office or Photoshop) are slow to launched, but...
3) ..once launched, those apps seem to run as expected...
...then the slow mech drive is the issue. Adding RAM won't help. I have the same model as you and here are app launch time hard data as I first doubled the RAM, then upgraded to an inexpensive solid-state drive:
—Base system as shipped:
4GB RAM and slow SATA 3GBps 500GB 5400rpm hard drive: Office 2008 and Photoshop Elements 12 took 15-18 seconds to be ready to use.
—First upgrade, double the RAM:
8GB RAM and slow SATA 3GBps 5400rpm hard drive: Office and Photoshop Elements took 15-18 seconds to be ready to use.
—Second upgrade, inexpensive solid-state drive
8GB RAM and fast SATA 6GBps 500GB SSD: Office and Photoshop Elements take under 4 seconds to be ready to use.
The SSD made the computer feel fast and new and I still use it for travel today over six years after the SSD install. Etrecheck scores show the old mech drive was moving data at 70-80MB sec. The SSD is doing nearly 500MB/sec.
⚠️ NOTE: I did my SSD upgrade in late 2017 while my 2012 MBP13 was still a supported model. That model is now 12 years old, and cannot run the latest macOS versions. Browser support is slipping away. The SSD install on a 12-year odl computer only makes sense if:
1) You look at this as a hobby or learning experience.
2) You do the work yourself. A pro is going charge you 1-2 hours of labor at US$65-80 an hour in my area (NW United States).
3) you cannot afford a new computer but can afford the SSD upgrade kit.
I just priced the exact 500GB kit I used and it is US$82 for the drive with install kit, and another $15 for the "must change" hard drive cable. You need to view the video instructions for the install to gauge your comfort level (SSD and cable). I took me about 45 minutes but I've been inside computers before.
If you are interested, post back and we can go from there.
NOTE: Best success with these conversions in your model seems to be with the OWC drive I used or with the Crucial MX series (not the older BX series). "Just any SSD" approaches have produced some very sad posts here.
