show that the set R of all multiples of 3 is a subring of Z .

Here's a start. There must be closure under additon and multiplication.

The set 3Z of all multiples of 3 is a subring.

Take a,b\in{3Z}; let a=3x and b=3y.

Then a-b=3(x-y)\in{3Z}

and ab=3(3xy)\in{3Z}