This is a job for Newton's 2nd Law! F = ma. We want to know the acceleration, so let's solve it for a, and get a = F/m. Now if we double the force, we'll have a' = 2F/m (where a' is the modified acceleration), and then if we decrease the mass by a half, we'd get a'' = 2F/(1/2*m) = 4F/m. We know the original acceleration was a = F/m, so let's sub that into the a'' equation and get: a'' = 4a, so a'' is 4 times the magnitude of our starting a.
