P3M : N4J :: R3P : ??

In a letter-and-number analogy of the form A : B :: C : D, one single transformation rule applies to the whole term at once: each letter moves a fixed number of places in the alphabet and the digit changes by a fixed amount. That combined rule is read off from the first pair and then applied unchanged, position by position, to the third term.

1. Compare the first pair P3M and N4J position by position: the first letter moves P to N (two places back in the alphabet), the digit moves 3 to 4 (one more), and the third letter moves M to J (three places back).

2. Apply the same three shifts to the third term R3P: shift its first letter R back the same two places, increase its digit by the same one, and shift its third letter P back the same three places.

3. R shifted back two places lands on P, the digit 3 increased by one becomes 4, and P shifted back three places lands on M — combining the three gives the fourth term.

Cross-check: re-reading the alphabet shifts from N back to P and from J back to M in the first pair reproduces the same two-place and three-place gaps used above, confirming the rule was read correctly before it was applied to R3P.

So the fourth term is P4M.