If FLOWER is written as GNQXFS, how is GARDEN written in that code?

Correct — D.
Rule: shift by position: +1, +2, +2, +1, +1, +1.

FLOWER → GNQXFS:
F+1 = G, L+2 = N, O+2 = Q, W+1 = X, E+1 = F, R+1 = S

GARDEN, same steps:
G+1 = H, A+2 = C, R+2 = T, D+1 = E, E+1 = F, N+1 = O
→ HCTEFO, option (d).

Why the others are wrong

• (a)
  HBSEFO — HBSEFO moves every letter +1. FLOWER → GNQXFS shows letters 2 and 3 move +2 (L → N, O → Q), so A must become C, not B.
• (b)
  HBSDFO — HBSDFO turns A into B and leaves D as D. Position 2 moves +2 and position 4 moves +1, so the code needs C second and E fourth.
• (c)
  HASEFO — HASEFO leaves A unchanged. Position 2 of FLOWER moves L → N, a step of +2, so A must become C.

In a positional code, write each letter's alphabet number over its code letter and read the step at each slot.

FLOWER to GNQXFS gives +1, +2, +2, +1, +1, +1. The steps belong to the positions, not the letters, so GARDEN takes the same steps in the same order.

The second slot settles it fast: A + 2 = C, and option (d) is the one with C second.

Key facts

• Positions used here: A = 1, D = 4, E = 5, G = 7, L = 12, N = 14, O = 15, R = 18.
• L → N and O → Q are both +2 steps.
• In positional coding each slot keeps its own step, whatever letter fills it.

Common traps

• Checking only F → G and applying +1 everywhere, which gives HBSEFO.
• Copying R → S from FLOWER: in GARDEN R sits in a +2 slot and becomes T.

No directly related past PYQ was found.