Let's analyze how "MOTHER" is coded as "OMHTRE".
The positions of letters in "MOTHER" are rearranged as follows:
- The first letter "M" is moved to the second position.
- The second letter "O" stays in the first position.
- The third and fourth letters "T" and "H" are swapped.
- The last two letters "E" and "R" stay in their original positions.
Now apply the same pattern to "FATHER":
- The first letter "F" should go to the second position.
- The second letter "A" stays in the first position.
- The third and fourth letters "T" and "H" are swapped.
- The last two letters "E" and "R" stay in their original positions.
So, the code for "FATHER" is "AFTREH". Answer: \(\boxed{D}\)