chuljang gagi jeone hyuga sincheongbuteo chwisohaeya haesseoyo.

Because 가다 has to be turned into a noun-like form before 전에 can attach to it.

• 가다 = to go
• 가기 = going / the act of going
• 전에 = before

So:

• 출장 가기 전에 = before going on a business trip

This is a very common pattern:

• 먹기 전에 = before eating
• 자기 전에 = before sleeping
• 출발하기 전에 = before departing

In this sentence, 가기 전에 modifies the action that had to be done first: canceling the leave request.

In Korean, 출장 가다 is a very common fixed expression meaning to go on a business trip. In everyday speech, people usually say:

• 출장 가다
• 여행 가다
• 학교 가다

rather than adding 을/를.

So 출장 가기 전에 sounds natural and normal.
Using 출장을 가다 would sound unnatural in most contexts.

휴가 신청 means a leave request or an application for time off.

Breakdown:

• 휴가 = vacation, leave
• 신청 = application, request

So 휴가 신청을 취소하다 means to cancel a leave request, not necessarily to cancel the vacation itself after it was fully approved. It focuses on the request/application process.

Here, 부터 adds the nuance of starting with, first of all, or at least this first.

So 휴가 신청부터 취소해야 했어요 suggests something like:

• I had to start by canceling the leave request
• The first thing I had to do was cancel the leave request

It often implies there may be other steps afterward, but this was the first necessary one.

Compare:

• 휴가 신청을 취소해야 했어요 = I had to cancel the leave request.
• 휴가 신청부터 취소해야 했어요 = I had to cancel the leave request first / to begin with.

They are similar, but not exactly the same.

• 먼저 = first, before anything else
• 부터 = starting with, beginning from

Compare:

• 휴가 신청을 먼저 취소해야 했어요
  = I had to cancel the leave request first.

• 휴가 신청부터 취소해야 했어요
  = I had to start by canceling the leave request.

먼저 focuses more on sequence.
부터 often highlights the starting point among several possible actions.

In many situations, both are possible, but 부터 gives a slightly stronger feeling of this was the first step.

In this sentence, 취소해야 했어요 most naturally means had to cancel.

Breakdown:

• 취소하다 = to cancel
• -아/어야 하다 = have to, must
• -았/었어요 = past tense, polite style

So:

• 취소해야 해요 = have to cancel
• 취소해야 했어요 = had to cancel

Depending on context, -아/어야 했어요 can sometimes sound like was supposed to or even imply regret, but the default reading is there was an obligation/necessity in the past.

So here the sentence most naturally says that before going on the business trip, canceling the leave request was something the speaker needed to do.

The main verb controls the tense of the sentence.

Here:

• 출장 가기 전에 = before going on a business trip
• 휴가 신청부터 취소해야 했어요 = had to cancel the leave request first

The past tense appears in the main predicate 해야 했어요, because that is the main event being described.
The before going part is just a time-setting clause.

This is very normal in Korean. Time clauses often do not need their own tense marking if the relationship is already clear.

The subject is omitted, which is very common in Korean.

Depending on context, it could mean:

• I had to cancel...
• He/She had to cancel...
• We had to cancel...

Korean often leaves out subjects when they are understood from the situation. In real conversation, listeners figure it out from context.

If you wanted to state it explicitly, you could say:

• 저는 출장 가기 전에 휴가 신청부터 취소해야 했어요.
  = I had to cancel the leave request first before going on the business trip.

Not necessarily. 전에 simply means before.

So 출장 가기 전에 tells you the cancellation happened earlier than the business trip, but it does not specify exactly how much earlier.

It could mean:

• right before leaving
• earlier that day
• several days beforehand

If you wanted to be more specific, Korean would use additional words like:

• 미리 = in advance
• 직전에 = right before

Korean usually puts background information before the main action.

So the sentence is structured like this:

1. 출장 가기 전에 = before going on the business trip
2. 휴가 신청부터 = starting with the leave request
3. 취소해야 했어요 = had to cancel

A natural way to think about it is:

• Before going on the business trip, [I] had to first cancel the leave request.

This order is very typical in Korean:

• time/background first
• object/details next
• main verb at the end

The wording specifically points to canceling the request/application, not directly the vacation as an event.

Because the phrase is:

• 휴가 신청 = leave request
• 휴가 신청을 취소하다 = cancel the leave request

If Korean wanted to focus more directly on canceling the leave itself, it might say something like:

• 휴가를 취소하다 = cancel the vacation/leave

So this sentence suggests an administrative action: the speaker had filed for leave, then had to withdraw that request because of the business trip.

했어요 is the polite, conversational ending.

Compare:

• 취소해야 했어요 = polite
• 취소해야 했다 = plain written/narrative style
• 취소해야 했습니다 = formal polite

So the sentence is in standard polite spoken Korean. It sounds natural in everyday conversation when speaking respectfully but not too formally.