In a certain code language, 'CASE' is written as 'FTBD' and 'CAKE' is written as 'FLBD'. How will 'CALF’ be written in that language?

Correct — C. Rule: move every letter one step forward, then write the result backwards.

CASE: C to D, A to B, S to T, E to F gives DBTF. Reversed, that is FTBD — the code the question prints.
CAKE: C to D, A to B, K to L, E to F gives DBLF. Reversed, that is FLBD — again the printed code.

Now CALF.
C to D, A to B, L to M, F to G gives DBMG.
Reverse DBMG and you get GMBD — option (c).

Why the others are wrong

• (a)
  GBDM — GBDM holds the right four letters in the wrong order. Undoing the shift on it gives F, A, C, L, which is neither CALF nor CALF reversed.
• (b)
  GBMD — GBMD reverses only the outer pair. Shifting CALF forward gives DBMG, and swapping just its first and last letters gives GBMD instead of the full reversal.
• (d)
  GMDB — GMDB leaves the tail in its original order. Its last two letters, D and B, are the images of C and A in that order, but a full reversal puts A's image before C's.

Two-step letter codes are common in this section: a shift, then a rearrangement. Fix the shift first on a letter that cannot be confused — here A becomes B in both given words.

Once the shift is settled, lay the shifted string beside the code. DBTF against FTBD is a straight reversal, and the second example confirms it.

Then apply the steps in the order you established. Reversing first and shifting afterwards happens to give the same answer here, but only because the shift is uniform.

Key facts

• Each letter moves one place forward: C to D, A to B, S to T, E to F.
• The shifted string is then written backwards, so DBTF becomes FTBD.
• CALF shifts to DBMG, which reverses to GMBD.

Common traps

• Applying the shift and stopping there, which gives DBMG
• Swapping only the outer letters instead of reversing the whole string

No directly related past PYQ was found.