jmc

The positive multiples of $3$ that are less than $20$ are $$3,6,9,12,15,18.$$The positive multiples of $6$ that are less than $20$ are $$6,12,18.$$Therefore, there are $6$ positive multiples of $3$ and $3$ positive multiples of $6$, so our final answer is $$3-6=-(6-3)=\boxed{-3}.$$