Question 352504
First, choose 2 out of 4 possible suits.
You can do this C(4,2) ways.
Once you have fixed the two suits, choose 3 out of 13 possible cards from one suit.  
You can do this in C(13,3) ways.
For the other suit, you can choose 3 out of 13 cards also in C(13,3) ways.
Therefore the total number of ways of drawing 3 cards of one suit and 3 cards of another suit is 
{{{C(4,2)*C(13,3)*C(13,3)}}}=6*286*286=490,776