Hard drive not found to reinstall macOS

Hello everyone!

I often browse this forum for solutions, but today I’m posting because I can’t find a solution anymore and I’m starting to despair.

Here’s the problem:

Having recently taken over my brother's MacBook Air, I decided to reformat it to delete everything and start fresh. However, with my little knowledge about Macs (I always use a PC...), I must have made a wrong move...
Now when I start the Mac, a round symbol with a line through it appears... So I restart with the CMD+R combination and access the OS Mountain Lion reinstallation, but when I try to start the installation, it can’t find my internal hard drive...
Yet in Disk Utility, it sees the drives but one is grayed out, and I don't know if I should erase it... :/

I’m relatively afraid of making other moves since I have really too little knowledge about Macs. So if any of you knows a solution, I would be happy to read it ;)

Thanks in advance.