hi i need help i have wiped the system but it will not let me put the Os back on so its completely useless:( trying to do it for my son ready for school

Internet/Network Recovery of El Capitan or Later on a Clean Disk

     If possible, back up your files before proceeding.

You will need a fast, working Internet connection, preferably, Ethernet. If you must use Wi-Fi, you will be asked to select your network and enter the network password. This procedure will install the current version of macOS that is compatible with your model.

1. Restart the computer. Immediately, at or before the chime, hold down the (Command-Option-R) keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the target drive (out-dented entry w/type and size) from the side list.
5. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to APFS (SSDs, only if installing Mojave or Catalina ) or Mac OS Extended, (Journaled.)
8. Provide a volume name, usually "Macintosh HD."
9. Click on the Apply button, then click on the Done button when it activates.
10. Quit Disk Utility and return to the Utility Menu.
11. Select Install OS X and click on the Continue button.

In the future, it's a good idea to know how to accomplish the desired goal before your proceed.

As I said earlier choose the target drive which would be the topmost entry, probably, labeled Apple SSD TS25...

SuperDrive is your DVD optical drive. Disk0s2 is the no longer working logical volume on the target drive. The bottoms stuff below the line represents mounted and unmounted disk images which are not relevant, here.

You Should choose the first one, 251 GB Apple SSD TS25 -

diskOs2