To solve this question, we need to identify the pattern in the given letter series and find the set of letters that complete it when placed in the gap.

Let's analyze the given letter series: __nmmn__mmnn__mnnm__

Pattern:
Looking at the series, we can observe the following pattern:
- The first two letters in each set are the same.
- The third letter in each set is the same as the fourth letter in the previous set.
- The fourth letter in each set is the same as the third letter in the next set.

Using this pattern, we can determine the missing letters in the series.

Analysis:
- The first set of letters is "__nmmn__". The first two letters are "n" and "m".
- The third letter in this set is the same as the fourth letter in the previous set, which is "m".
- The fourth letter in this set is the same as the third letter in the next set, which is "n".

- The second set of letters is "__mmnn__". The first two letters are "m" and "m".
- The third letter in this set is the same as the fourth letter in the previous set, which is "n".
- The fourth letter in this set is the same as the third letter in the next set, which is "n".

- The third set of letters is "__mnnm__". The first two letters are "m" and "n".
- The third letter in this set is the same as the fourth letter in the previous set, which is "n".
- The fourth letter in this set is the same as the third letter in the next set, which is "m".

Now, to complete the series, we need to find the set of letters that follows the same pattern.

Solution:
Based on the pattern observed, the missing set of letters should have the following characteristics:
- The first two letters should be "n" and "n".
- The third letter should be the same as the fourth letter in the previous set, which is "m".
- The fourth letter should be the same as the third letter in the next set, which is "m".

Among the given options, only option 'A' (nnmm) satisfies these characteristics. Therefore, the correct answer is option 'A' (nnmm).