The first thing that jumps out at me here is the "-ing" modifier at the beginning of the sentence. The underlined portion has to begin with somebody who can actually speak, like Adam Silver...
Quote:
(A) Adam Silver, the league's commissioner, rejected the idea of expanding the regular-season schedule beyond the six months of games that have been planned for the 2017-18 season and that the league could reduce the number of games teams play on consecutive nights.
This looks fine in terms of the "-ing" modifier. "Number of games" is fine, too. It's just that the parallelism is weird: "... the six months of games that have been planned... and that the league could reduce the number of games." Huh? Sure, I suppose the two "thats" are sort of parallel structurally, but they also make absolutely no sense as two parts of a list. Eliminate (A).
Quote:
(B) the idea of expanding the regular-season schedule beyond the six months of games that have been planned for the 2017-18 season was rejected by league commissioner Adam Silver, but he said the league could reduce the amount of games teams play on consecutive nights.
This one is a pretty easy elimination: "speaking" can't modify "the idea." Also, "amount" can only be used to modify non-countable nouns. Eliminate (B).
Quote:
(C) league commissioner Adam Silver rejected the idea of expanding the regular-season schedule beyond the six months of games that have been planned for the 2017-18 season but said the league could reduce the amount of games teams play on consecutive nights.
"Amount" is the only real problem here. Eliminate (C).
Quote:
(D) the expansion of the regular-season schedule beyond the six months of games planned for the 2017-18 season was rejected by league commissioner Adam Silver, but he said the league could reduce the games played by teams on consecutive nights.
This is a similar error as in (B): "speaking" can't modify "the expansion", because expansions can't speak. Also a little bit weird to say "reduce the games played" -- I think we're trying to reduce the number of games, not the actual games themselves.
Quote:
(E) league commissioner Adam Silver rejected the idea of expanding the regular-season schedule beyond the six months of games that have been planned for the 2017-18 season but said the league could reduce the number of games teams play on consecutive nights.
This one looks fine, I guess. There's no problem with the "-ing" modifier anymore, and "number of games" is correct. (E) is the answer.