To find the length of side \( y \) in a right triangle where one leg is 8 inches and the hypotenuse is 12 inches, you would use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( a \) and \( b \) are the legs of the triangle and \( c \) is the hypotenuse.
In this case, you can plug in the values:
\[ 8^2 + y^2 = 12^2 \]
So, the correct equation to find the length of side \( y \) is:
\( 8^2 + y^2 = 12^2 \)
Thus, the correct response from the options you provided is:
\( 8^2 + y^2 = 12^2 \) (8 squared plus y squared is equal to 12 squared).