The following is a multi-step reaction. the rate-limiting step is unimolecular, with a as the sole reactant.

I) from the information given, that the rate-limiting step is unimolecular with A as the sole reactant, the rate law of the reaction is therefore; 
Rate = k[A]
If you double the concentration of A, the rate of the reaction wil also double to 0.008 M/s

ii) The concentration of B has no effect on the rate of reaction, and therefore halving the concentration of B, will not change the rate of reaction. Thus the reaction rate remains 0.0040 M/s

iii) Increasing the concentration of A by 4-fold also increases the rate of reaction by 4-fold to (0.0040 ×4) = 0.016 M/s. This is because the rate of reaction depends on the concentration of A, therefore any change in this concentration affects the rate of reaction, such that an increase in the concentration of A cause a corresponding increase in the rate of reaction and vice versa.