let x and y be the positive numbers and x>y

one positive number exceeds another by 4

x = y + 4

and their product is 96

x*y = 96

(y +4)y = 96

by solving we find

y = 8

click here to see the step by step solution of the equation

x = 8 + 4

x = 12

indeed 12*8=96

the two numbers are 12 and 8.