Due to heavy rains, water had …….. in the low lying areas.

Not quite sure what your question is. From the choices given, A seems most appropriate to me. I might choose "collected" or "accumulated" if I were writing the sentence.

D is too obvious to be noted, it's not much different than saying "if rain falls from the sky, it hits the ground."

C has a connotation of deliberate, intentional activity. "Assembly" tends to be a conscious and deliberate production, and not really applicable to the movement of water.

B works, I guess, but "stagnation" is not really "due to" heavy rains. Ponds can result from a rainfall and surface run-off. But, if that's what I meant to emphasize, I would probably just say "Ponds (or "puddles") were created in low spots"

Accumulated
Pooled
Flooded