(b)
The rate law for the reaction is as
r=$\frac{dx}{dt}$=k(A)$(B)^{2}(C)^{0}$=$k(A)(B)^{2}$
on increasing the concentration of A,B and C two times.
r’=$\frac{dx}{dt}$=k(2A)$(2B)^{2}(2C)^{0}$
=8k(A)$(B)^{2}$
Thus, the rate increases eight times.