The word TELEPHONE consists of 9 letters, with the letters P and L fixed at the ends. This leaves us with 7 letters: T, E, E, E, H, O, N to arrange in the middle.

First, calculate the number of ways to arrange these 7 letters. Since there are 3 E's, the number of distinct arrangements is given by:

\(\frac{7!}{3!}\)

Calculating this gives:

\(\frac{7!}{3!} = \frac{5040}{6} = 840\)

Since P and L can be at either end, we have 2 possible arrangements for the ends (P at the start and L at the end, or L at the start and P at the end). Therefore, multiply the number of arrangements by 2:

\(840 \times 2 = 1680\)

Thus, the total number of ways to arrange the letters is 1680.