SOLUTION: If 6 is added to a number and then subtracted from the same number, the product of the sum and the difference is 189.What is the number?

If 6 is added to a number N, we get the sum N+6.

If 6 is subtracted from the same number N, we get the difference N-6.

The product (multiplication) of this sum and this difference is (N+6)(N-6)  

But we are told that

So we have the equation

                    (N+6)(N-6)=189

Can you simplify and solve that quadratic? If not post again
asking how.

You get N = 15 and N = -15

Nothing was said about the number not being negative, so both answers
are solutions.

Edwin