$LHS=A-(B-C)= A-(B \cap C') = A \cap (B \cap C')'=A\cap(B' \cup C)=(A \cap B') \cup (A \cap C)$
$RHS=(A-B)\cup C= (A \cap B') \cup C= (A \cup C)\cap (B' \cup C)$
Thus $(1)$ is wrong.
$LHS=A-(B\cup C)= A \cap (B \cup C)' = A \cap (B' \cap C')=A \cap B' \cap C'$
$RHS=(A-B)-C= (A \cap B') - C = (A \cap B') \cap C'=A \cap B' \cap C'$
Thus $(2)$ is correct.
$\therefore$ Option $C.$ is correct.