Word: E Q U A L I T Y
Positions: 1 2 3 4 5 6 7 8
Step 1: Swap 1st and 5th letters: E \(\leftrightarrow\) L
New positions: L Q U A E I T Y
Step 2: Swap 2nd and 6th letters: Q \(\leftrightarrow\) I
New positions: L I U A E Q T Y
Step 3: Swap 3rd and 7th letters: U \(\leftrightarrow\) T
New positions: L I T A E Q U Y
Step 4: Swap 4th and 8th letters: A \(\leftrightarrow\) Y
New positions: L I T Y E Q U A
Step 5: Find the third letter from the right end:
Letters from right end: A (1st), U (2nd), Q (3rd)
Hence, the letter is \(\boxed{Q}\).