Result: $(A\times C)-(B\times C)\subseteq (A-B)\times C$
Proof: Let $(x,y)\in (A\times C)-(B\times C)$. Then $(x,y)\in A\times C,\implies x\in A,y\in C$. Since $(x,y)\notin B\times C, x\notin B$. Thus $x\in A-B$ and hence $(x,y)\in (A-B)\times C$
Result: $(A\times C)-(B\times C)\subseteq (A-B)\times C$
Proof: Let $(x,y)\in (A\times C)-(B\times C)$. Then $(x,y)\in A\times C,\implies x\in A,y\in C$. Since $(x,y)\notin B\times C, x\notin B$. Thus $x\in A-B$ and hence $(x,y)\in (A-B)\times C$