comes back from her business trip. Until - use comes back/ came back , don't use will come back / would come back next month - use comes back/ will come back, don't use came back/ would come back Until/next month - comes back

This is tricky because it is a relative clause embedded in reported speech. Let's take it one step at at time. First, the relative clause without reported speech: She will not be available until next month, when she COMES back from A business trip. "Will come back" is wrong. The rule here that in a sentence with a main clause and a subordinate clause expressing time, you never use "will" in the subordinate clause. For the same reason, "would come back" is also wrong. "Came back" is wrong because the relative clause refers to the future, not the past. Now, you just have to put the sentence above into the reporting clause "I found out that..." As you know, in reported speech we shift all of the tenses back one step. So in the first clause ("I found out that she will not be available") "will" changes to "would." However, if you do that in the second clause ("when she comes back from a business trip"), the sentence won't make sense because "when she comes back" refers to the future, not the present. So it is more natural not to shift the tense for that clause. The result is: I found out that she would not be available until next month, when she comes back from a business trip.

would come back i think :)

would come back