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A.  If the third side is the longest side, then we're looking for the hypotenuse.  By definition of Pythagorean Theorem:

The square of hypotenuse is equal to the sum of the squares of the two shorter legs/sides. 

Then, with c as the hypotenuse
c² = 10² + 6²
c² = 100 + 36

 \sqrt{c ^{2} } =  \sqrt{136}
c =  \sqrt{(4)(34)}
c = 2 \sqrt{34} inches

B.  If the third side is a shorter leg, then, with b as the shorter side, and c ans the hypotenuse, then:
b² = c² - a²
b² = 10² - 6²
 \sqrt{ b^{2} } =   \sqrt{100-64}
b =  \sqrt{64}
b = 8 inches

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