Given that x-y = 12 and 1/x -1/y = 3, we are to find x*y.

=> 1/x -1/y = 3

=> [xy/1] [1/x -1/y] = 12

=> (y - x) /xy = 3

=>  3xy = y - x

=>  -3xy = x - y

=>  -3xy = 12

=>  (-3xy)/-3 = 12/-3

=> xy = -4

The correct answer is x * y = -4

We have the equations x - y = 12 and ( 1/x) - ( 1/y) = 3. We have to determine x*y.

( 1/x) - ( 1/y) = 3

=> y/xy - x/xy = 3

=> (y - x) = 3xy

but we know x - y = 12

=> y - x = -12

(y - x) = 3xy

=> -12 = 3xy

=> xy = -12/ 3

=> xy = -4

The required value of xy = -4