Rate = k[A][B]
This means the rate is directly proportional to the concentration of A and B, i.e. first order in both.
So, if [A] doubles, and [B] stays the same, the rate will double.
If [B] doubles, and [A] stays the same, the rate will double.
If both [A] and [B] double, the rate will increase by 4 times.
You can see this mathematically from the rate law as follows:
Rate = k[2][2] = 4k and since k is constant, the rate will be 4x what it was when the [A] and [B] were each 1.
