Let me focus on the first rhythm only:
The sixteenth triplet takes the place of an eighth note, which together with the quarter note sits in a triplet. Thus, the quarter takes up 2/3rds of a normal quarter note value, and the three notes in the triplet each take up 1/9th of a quarter note value. Thus, together the larger triplet takes up one quarter note (2/3 + 1/9 + 1/9 + 1/9 = 1 quarter note). This reading corresponds to the following equivalent notation:
If you want to practice this slowly, you can count the quarter note as 6/9, with the three sixteenth notes as 1/9 each.
Alternatively, you can start by replacing the three sixteenths by a single eighth note, and playing the outer triplet rhythm first:
Then you replace the single eighth note by a sixteenth note triplet. This second interpretation is closer to the genesis of the rhythm, and presumably the reason the notation with embedded triplets (as opposed to the alternative one with nonuplets) was chosen.