In weight, $$45$$ mice $$=3\times (15$$ mice$$)=3\times (2$$ cats$$)= 2\times (3$$ cats$$)=2\times (2$$ dogs$$)= 4$$ dogs.  On Planet Pythagoras, the people use a different money system to us.  two pog is worth six pings. 
If $$2$$ dogs weigh as much as $$3$$ cats, and $$2$$ cats weigh as much as $$15$$ mice, how many dogs weigh as much as $$45$$ mice? 
1) $$3$$ 
2) $$4$$ 
3) $$6$$ 
4) $$9$$ 