Every right triangle obeys to the Pythagorean theorem, which states that the hypotenuse squared equals the sum of the legs squared.
In your case, the right triangle is also isosceles, so both legs are 6 units long. This means that we can compute the hypotenuse [tex] h [/tex] as follows:
[tex] h^2 = 6^2+6^2 = 36+36 = 72 [/tex]
This means that [tex] h = \sqrt{72} [/tex], which can be simplified to [tex] 6\sqrt[2} [/tex]
so is a right-triangle, which means it has a right-angle, the hypotenuse is the longest leg, and it has two more legs, well, is an isosceles triangle, which means it has two sides that are twins, well, it can't be the hypotenuse certainly, so the other two legs must be twins, and we know they're 6 units long each.
[tex] \bf \textit{using the pythagorean theorem}
\\\\
c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}
\qquad
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}
\\\\\\
c=\sqrt{6^2+6^2}\implies c=\sqrt{6^2(1+1)}\implies c=\sqrt{6^2(2)}\implies c=6\sqrt{2} [/tex]
