I agree that both of them seem to make sense, but "capacity" is definitely the right answer. Capacity is the word we use to describe a factory that is producing as much as it can. Usually, "full time" is used to describe a person who is working a full 40-ish hour work week. Also, "full time" is not preceded by "at", but "full capacity" is preceded by "at".

Hi Mary, Chris is correct. In fact, only "capacity" suits the sentence structure and makes sense. In your sentence, the machines in the factory are operated at full speed to churn out as many pieces of clothing as possible. We use the expression "full capacity" to mean the potential output that can be realised by some equipment in a facility. There is such an expression as "full time", but it is used to describe someone who is employed on a regular basis and works for the whole of that person's available working time. So, clearly, "time" does not match the meaning of your sentence. Another reason is that "full time" does not match the sentence structure: "Workers are working full-time to produce clothes as fast as possible" but we do not say "Workers are working at full-time..." ("working" is a verb in the continuous aspect and is followed by an adverb "full-time" to describe how the workers are working. Thus, there is no necessity for a preposition "at" between them.) In a nutshell, a person can work "full-time" or "part-time" but a factory can operate at "full capacity" or "half its capacity". Just as a side remark, a room can also be filled to "full capacity" with people or a container can be filled to "full capacity", meaning to the brim. I hope this helps.

full capacity

It says "fast" so maybe the answer can be "time". But I am not sure...