For your first question you are multiplying a binomial by a binomial. You can do this by applying the distributive property you are already familiar with and reduce the problem to one of multiplying a binomial by 2 monomials. I will illustrate this:
= (x)(x + 2) + (1)(x + 2)
= x2 + 2x + x + 2
= x2 + 3x + 2
For your second question you need to remember that if 2 numbers multiplied together result in zero, then either one of the terms is zero, or both of the terms is zero. You need to find which values for x will result in the whole expression being zero. So either (2x - 1) is equal to zero, or (x - 4) is equal to zero (or both of them are). Can you see how to solve for which values of x make (2x-1)(x-4)=0 now?
Hope this helps,