Explanation:

- To encode the word PAYMENT, each letter is replaced by numbers. P is coded as 7, A as 1, Y as 7, M as 4, E as 5, N as 5, and T as 2. This pattern must be used to code YOUNGER.

- Let's decode and encode each letter of YOUNGER using the same logic.

- The first letter, Y, was previously coded as 7.

- Following the assumed pattern logic, O could be treated similarly to another coded letter, U may refer to the steps from N, and so on to R.

- Checking each option:

- Option 1: 7153540 doesn't fit the pattern for YOUNGER.

- Option 2: 2121751 doesn't fit the pattern either.

- Option 3: 7635759 could potentially work with a consistent pattern applied.

- Option 4: 5514758 does not seem to fit using our logic.

- Correct coding for YOUNGER appears to be Option 3: 7635759

-