x = 8.
Why? Simply use the Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are legs of the right triangle, and c is the hypotenuse! We already have c = 10 and a = 6, so we can just solve for the other side b.
6^2 + b^2 = 10^2
36 + b^2 = 100
b^2 = 64
b = 8