Qual é a diferença entre
We live in groups, in 'the' way that lions gather in prides and ants form colonies
e
We live in groups, in 'a' way that lions gather in prides and ants form colonies
?Podes indicar apenas respostas exemplo.

@hhoc2000 not really, no. "We live in groups, in a way that lions gather in prides" is unnatural because what you're referring to is the group nature of prides/colonies specifically, not anything else. Whether it's fast or slow, there's no material difference in the way that lions gather in prides.

This is different to the dancing example because dancing is inherently different depending on how you do it — a slow waltz and a samba are not the same dances and thus the way you dance them is not the same. With lions gathering into prides, the relevant factor is that they end up in a pride, and so there's only one way for that to occur: by gathering into groups. We don't differentiate prides/colonies based on HOW they were formed, but we do differentiate dances based on HOW you dance.

The exact nature of the gathering is irrelevant to the conversation, because the focus is on the resulting pride/colony/group. It is confusing but my overall point is that while both "a" and "the" are possible for the dance sentence, only "the" is possible for the groups sentence.

For the answering a question sentence, "in a way that" is fine because there are multiple ways to answer a question (in this case), and there are multiple ways to get someone to understand something, so "a" is fine because it's one way of answering out of several. The answer to a question is differentiated based on the nature of the answer e.g. if it's long, short, uses analogies, etc., so "a" can be used here because there are multiple different ways. "in the way that" is also fine because it implies you've picked one specific way of the multiple ways to answer the question in. I think most people would say "a" because it recognises the fact that there may be multiple ways to get the person to understand, but both are acceptable.

I really apologise if my explanation is not clear, the difference between "a" and "the" in English can border on completely arbitrary at times and so it can be difficult to give an answer more useful than "because we do".