AS rate =K[A][B] where [A] = conc of A
[B] = conc. of B
conc. = no of moles / volume
therefore we decrease the volume of vessel to1/4 th initial volume .the conc. of A and B both will increase by 4 times { conc. is inversely proportional to volume } .
so final conc. of A will become = 4[A]
final conc. of B will become = 4[B]
final rate of rxn = k{4[A]*4[B] }
= 16k[A][B]
= 16 {initial rate of reaction}