Well, tackle Brahms' 51 Exercises, and you'll have 3 against 4 in both hands engrained. And wait 'til you get to 4 against 5 and the more ridiculous ones.

But really, I took both approaches. The mathematical and the natural, "autopilot" approach. In the end it really was a mixture of the two before I got it down.

So let's start with the mathematical. Get your grammar school math out and what's the lowest common multiple of 3 and 4? 12. So subdivide the beat into 12 sections. You have the triplets playing on 1,5 and 9. The 16ths are playing on 1,4,7, and 10. Draw it out, and you'll see how the beats fit together. Now try drumming it at a slow pace on your knees. You should discover that drumming the rhythm isn't too difficult.

Now, try doing the same with your fingers and a simple pattern. I like playing c-d-e-f over and over with my left hand, and c-d-e with the right. Start slowly to see how the beats should feel together.

Unfortunately, this approach doesn't work very well once you speed the tempos up. However, it seems to help with the muscular memory of how the two parts should fit together. What I did afterwards was to put left hand on "autopilot" and play the four notes over and over and over, and trying to fit those triplets cleanly over the 16ths. Initially, you probably will be able to fit the 3s over the 4, but with a tendency to shave different parts of the 3s, thereby not getting true triplets. I had the tendency when learning 3 over 2, to play the 3 as dotted eighth, dotted eight, eight, rather than a true triplet. I find the same thing happening with 4 over 3.

So then just practice the pattern over and over again, try to keep those triplets clean. Eventually, you should be able to speed up the tempo and once you get it, it is like riding a bike. You get it!