What is the largest multiple of 3 and 7?

There is no such number.

Since if x were the largest multiple of 3 and 7 then what about 2x?

2x would be a multiple of 3 since x is a multiple of 3;

2x would be a multiple of 7 since x is a multiple of 7; and

2x is bigger than x. So x cannot be the largest.