Geminiii
Option A is correct.
When I opened the hood and saw smoke pouring from the engine, I realized that I forgot to add oil.
(A) realized that I forgot to add oil. Correct
(B) had realized that I forgot to add oil. - past
(C) had realized that I forgotten to add oil. - past
(D) realized that I would forget to add oil. - would is confusing
(E) realized that I had forgotten to add oil. - past
Official Explanation
Verb tenses must be in proper sequence. When two or more events have taken place, are taking place, or will take place at the same time, their tenses must be the same. If two events have taken place in the past but one event occurred prior to the other, the later of the two events must be in the past tense, and the earlier of the two must be in the past perfect tense (had plus the past tense of the verb). In this sentence, the “opening,” the “seeing,” and the “realizing” all took place in the past at the same time and therefore should all be in the (simple) past tense. So choices (B) and (C) (with had realized, which is the past perfect tense) are wrong. The “forgetting” also took place in the past but prior to the other three events and therefore should be in the past perfect tense (had forgotten). So choices (A), (B), and (D) are wrong.
The correct answer is (E).
Hope it helps