Answer
a) $AB$ is defined with size 3x5
b) $BA$ is not defined
c) $AC$ is defined with size 3x4
d) $CA$ is not defined
e) $BC$ is not defined
f) $CB$ is defined with size 4x5
Work Step by Step
If $U, V$ are matrices of sizes $u_r \times u_c$ and $v_r \times v_c$ respectively, $UV$ is defined if and only if $u_c=v_r$. The size of $UV$ is $u_r\times v_c$. So for $A, B, C$ with sizes 3x4, 4x5, and 4x4 respectively,
a) $AB$ is defined with size 3x5.
b) $BA$ is not defined.
c) $AC$ is defined with size 3x4.
d) $CA$ is not defined.
e) $BC$ is not defined.
f) $CB$ is defined with size 4x5.