how do you solve for the possible answers for log 16 base x+2 is equal to 2? What is the product of all possible solutions?

You must remember that log_{b}x=y implies b^{y} = x.

so log_{(x+2)}16 = 2 implies (x+2)^{2}=16.

Next (x+2)^{2 }= x^{2}+4x+4

So x^{2}+4x+4-16 = 0

Then x^{2}+4x-12 = 0.

Using the quadratic formula (-b+√b^{2}-4ac) / 2a gives us -6 and +2.

Therefore (-6)(2) = -12