The product of two numbers is 32. The first number, x, is one-half of the second number, y.

Product means multiply so ...

the product of two numbers is 32

=" x * y = 32

x is one-half of the second number, y

which means x = 0.5 y

="0.5y * y = 32

0.5y^2 = 32

: both side my 0.5

="y^2=64

square root both sides

="y = sqrt (64)

y=8

and

x = 0.5 (8) = 4