Because of the little square in corner of one angle in the triangle, you know that angle is 90º and that means this is a right triangle.
Becuase it's a right triangle, you can use the Pythagorean Theorem.
"The sum of the squares of the legs equals the square of the hypotenuse."
This is usually stated as [tex]a^2+b^2=c^2[/tex]. The key is that [tex]c[/tex] is the side length opposite the 90º angle.
OK, so in your case, you have
[tex]x^2+8^2 = 12^2[/tex]
Solving that would look like this:
[tex]\begin{aligned}x^2+8^2 &= 12^2\\[0.5em]x^2+64 &= 144\\[0.5em]x^2 &= 80\end{aligned}[/tex]
Then you square root each side
[tex]x = \sqrt{80}[/tex]
(Techincally it's [tex]x = \pm \sqrt{80}[/tex], but a negative value doesn't make sense here.0
Throw that into a calculator and you get x ≈ 8.94.
