For a reaction 2A+B→products, doubling the initial concentration of both the reactants increases the rate by a factor of 8, and doubling the concentration of B alone doubles the rate. The rate law for the reaction is

2A+B→ProductsAccording to question: Rate of reaction of ∝[B] as increase in rate is double when [B] is doubled. Rate of reaction ∝[A]2[B] as increase in rate is 8 times when concentration of both reactant is doubled. It means that order of reaction is 3 and overall rate of  reaction should be r=K[A]2[B]