How do I solve for x here?

You need to write a^2 + b^2 = c^2   and fill in what you know

12^2+x2=(8+x)2   Simplify both side
x^2+144=x^2+16x+64         Subtract x^2 from both sides.
x^2+144−x^2=x^2+16x+64−x^2144=16x+64    Subtract 64 from both sides.
16x+64−64=144−64
16x=80    Divide both sides by 16.
16x/16=80/16
x=5