There is a special approach to 4:3 rhythm in African music, but I will try to answer with a Western, classical approach, because that seems to be the style of your notation example.
The polyrhythm grid for 4:3 is...
RH | 1 . . 2 . . 3 . . 4 . . |
LH | 1 . . . 2 . . . 3 . . . |
Count | 1 e + a 2 e + a 3 e + a |
You basically need each hand to get 12 subdivisions of the bar so you can get group by 3 and 4 in each hand. Then we see exactly where the RH notes fall in the counting.
When the count is placed into each hand we get...
RH | 1 . . . . . . . . e . . |
LH | 1 . . . 2 . . . 3 . . . |
The trouble is whether the triplet figure in your example is a tuplet in a duple meter or if the meter is actually compound like 12/8.
If it's 3 8ths in the bass in compound meter, I think it's easier to manage the counting, because the e
in the right hand is just an even 16th note subdivision of the basic beat.
If the meter is duple, the triplet will have a hemiola feel, which to me feels like a kind of stretching or squeezing of the tempo. That makes it harder to get the timing of the e
in the right hand precise.
The overall tempo becomes an issue too. If you actually count this precisely, those notes are being counted at a 32nd level of subdivision. If the tempo is allegro that's really fast!
(I'm just starting to practice these polyrhythms myself and this metrical/tempo context seems like the big challenge.)
While it isn't mathematically correct, you could time that 16th in the right hand at the place where a 16th would be in the left hand, like this...
... the count would be 1 2 3 +
.
Again, that isn't mathematically correct, but if you keep the beat steady and the RH 16th comes between the LH 3 and 1 of the next bar and it is more or less correct. My understand is historically Baroque and Classical era performers would have done it this way. Or, they would have place the RH 16th at the same time as the LH 3.
Re. exercises.
I tried playing polyrhythms over various patterns. Sometimes I just play one repeating note in each hand. Sometimes I break up a chord between my two hands. Both can get monotonous quickly. Playing a descending 6/3 chord sequence is a nice way to get movements and changing tones...
...you can play around with the chords of that pattern. Try seventh chords, change the mode to minor, use an exotic mode, break out to form a half cadence, etc.
Absolutely use a metronome! If you don't, your tempo can easily drift.
Again, I'm just starting to practice these rhythms myself. I'm not a teacher. But, everything above has helped me a lot.