In a certain code language, ‘DAYS’ is coded as ‘6958’ and ‘LADY’ is coded as…

Concept: In letter-coding puzzles, when two words share some letters, compare their numeric codes: digits that appear in both codes correspond to the letters common to both words (though the exact one-to-one order among those shared letters may not be pinned down from two words alone), while a digit that appears in only one code must belong to the letter that is present in only that word.

1. Write down both coded words: DAYS → 6958 and LADY → 2958.

2. List the letters of each word: DAYS = {D, A, Y, S} and LADY = {L, A, D, Y}.

3. Identify the letters common to both words: A, D, and Y appear in both DAYS and LADY.

4. Identify the digits common to both codes by comparing 6958 and 2958: the digits 9, 5, and 8 occur in both codes, while 6 occurs only in DAYS's code and 2 occurs only in LADY's code.

5. Match the letters that appear in only one word to the digits that appear in only one code: S is the only letter in DAYS that is absent from LADY, so S corresponds to 6 (the only digit in DAYS's code absent from LADY's code); L is the only letter in LADY that is absent from DAYS, so L corresponds to 2 (the only digit in LADY's code absent from DAYS's code).

6. Therefore, the code for L is 2.

Cross-check: The three shared letters A, D, and Y must together account for the three shared digits 9, 5, and 8 — exactly matching in count. This confirms there is no leftover digit to reassign, and that 6 and 2 are correctly isolated as the unique codes for S and L respectively.