You have an acidic solution and add equal amounts of a basic solution. What are the products of this reaction?

Depends on the pH of the acidic and basic solutions, but if by equal amounts you meant an acid of 0 for example and a base of 14 for example, then those two solutions mixed would have a pH of 7 meaning the product is a neutral solution. This is of course only true if I understood you question correctly, and didn't somehow miss an important factor.