\[
(A)\rightarrow(II)
\]
Hands full = very busy.
\[
(B)\rightarrow(III)
\]
Hand in glove with = closely associated.
\[
(C)\rightarrow(IV)
\]
Grease someone's palm = bribe someone.
\[
(D)\rightarrow(I)
\]
Leave in the lurch = abandon someone in difficulty.
Thus,
\[
(A)-(II),\ (B)-(III),\ (C)-(IV),\ (D)-(I)
\]
\[
{\text{Option (C)}}
\]