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