Odd man out.

Concept:

Each option is a set of three letters. Convert every letter to its position in the alphabet (A = 1, B = 2, ... Z = 26), then find the two successive gaps within each triplet. Groups built on the same underlying rule share a common relationship between these two gaps -- here, the second gap is exactly 2 more than the first (the gap increases by a fixed amount from step one to step two). The group whose gaps do not follow that increasing relationship is the odd one out.

Application:

1. ADG: A = 1, D = 4, G = 7 -> gaps = 4-1 = 3 and 7-4 = 3. Second gap - first gap = 3-3 = 0 (no increase).

2. DGL: D = 4, G = 7, L = 12 -> gaps = 7-4 = 3 and 12-7 = 5. Second gap - first gap = 5-3 = 2.

3. UVY: U = 21, V = 22, Y = 25 -> gaps = 22-21 = 1 and 25-22 = 3. Second gap - first gap = 3-1 = 2.

4. BDH: B = 2, D = 4, H = 8 -> gaps = 4-2 = 2 and 8-4 = 4. Second gap - first gap = 4-2 = 2.

Cross-check:

DGL, UVY and BDH each show the second gap exceeding the first by exactly 2, confirming one consistent 'gap increases by 2' rule across three separate groups -- too precise a match across three different triplets to be coincidence. ADG is the only group whose two gaps stay equal (an increase of 0, not 2), so it breaks this shared rule.

Result:

ADG is the odd one out.