The pythagorean theorem says a^2 + b^2 = c^2 when a and b are the sides of the right triangle and c is the hypotenuse (longest side, opposite the 90 degree angle).
so if 8^2 + 6^2 = 10^2, then it's a right triangle.
8^2 + 6^2 = 64 + 36 = 100 = 10^2, so yes, this is a right triangle.