UPDATE: I added an intermediate step that will help illustrate what’s going on here.
Some helper exercises for my right hand lead 16th note method. The stickings for that are irregular, unless you’re relating them to the triplet form of the system. We’ll run them together here, hopefully finding a similar movement between systems.

Notice on situations 1 and 2 you add the opposite hand in the middle of a double:
RLL becomes RLRL / LLR becomes LRLR
On situation 3 you just double the left:
RLR becomes RLLR
Situation 4 is an odd case, just remember there are three doubles on the snare drum:
RLLRLR becomes RLLRRLLR
Situations 5, 6 and 7 just use the paradiddle inversions— or 5 and 6 alternate, if you’ve been alternating in those situations.
