يبدو المدرب مشغولا قبل المباراة.

Here يبدو means seems or appears. In this sentence, seems is usually the most natural English equivalent.

• يبدو is the imperfect/present form of a verb meaning to appear / to seem
• Literally, the structure is something like appears the coach busy before the match
• Natural English rearranges this as The coach seems busy before the match

So يبدو is the key verb that gives the sentence its present-time meaning.

Because Arabic very commonly allows, and often prefers, verb-first word order.

So:

• يبدو المدرب مشغولا = The coach seems busy
• Literally: Seems the coach busy

This is a normal Arabic sentence pattern. In Modern Standard Arabic, both of these are possible:

• يبدو المدرب مشغولا
• المدرب يبدو مشغولا

They are both correct, but the first one sounds more naturally verbal and is very common in formal Arabic.

المدرب means the coach.

The prefix الـ is the Arabic definite article, equivalent to the in English. So:

• مدرب = a coach / coach
• المدرب = the coach

Since the meaning already refers to a specific coach, Arabic uses المدرب.

Because المدرب is the subject of the verb يبدو.

In fully vowelled Arabic, it would be:

• يبدو المدربُ مشغولًا قبلَ المباراةِ

The ـُ ending on المدربُ marks the nominative, which is the normal case for the subject of a verb.

So:

• المدربُ = the subject, therefore nominative

In normal unvowelled writing, you usually do not see that ending written out, but grammatically it is still there.

Because the word is functioning as a description of the subject after the verb seems/appears, and in this structure Arabic commonly puts that descriptive word in the accusative.

Fully vowelled, it is:

• مَشْغُولًا

That final ـًـا shows an indefinite accusative ending.

So the pattern is roughly:

• يبدو + subject + descriptive accusative

Example:

• يبدو الرجلُ سعيدًا = The man seems happy
• يبدو المدربُ مشغولًا = The coach seems busy

This is one of the details that feels different from English, because English does not mark this kind of word with case.

Because مشغولا is not an adjective directly attached to المدرب inside one noun phrase. It is a predicate-like description, not part of the busy coach.

Compare:

• المدرب المشغول = the busy coach
  Here المشغول is a regular adjective modifying المدرب, so it must also be definite.

But in your sentence:

• يبدو المدرب مشغولا = The coach seems busy

Here مشغولا is not the adjective inside the noun phrase. It is the description being said about the coach, so it stays indefinite.

It agrees with المدرب in gender and number.

Since المدرب is:

• masculine
• singular

the describing word is also masculine singular:

• مشغولًا

If the noun changed, the description would change too. For example:

• تبدو المدربة مشغولةً = The female coach seems busy
• يبدو المدربان مشغولين = The two coaches seem busy
• يبدو المدربون مشغولين = The coaches seem busy

So even though the case ending may change because of sentence structure, agreement in gender and number still matters.

قبل المباراة means before the match or before the game.

Grammatically:

• قبل = before
• المباراة = the match

This expression gives a time relationship: before the match.

قبل is commonly treated as a time noun/adverbial expression, and the noun after it comes in the genitive.

So in full vowelled form:

• قبلَ المباراةِ

where:

• قبلَ has its own case based on its role in the sentence
• المباراةِ is genitive because it comes after قبل in this construction

Because it comes after قبل in an iḍāfa-like construction: قبلَ المباراةِ.

This is very common in Arabic with words like:

• قبل = before
• بعد = after
• أثناء = during

The noun that follows is put in the genitive.

So:

• قبلَ المباراةِ = before the match
• بعدَ الدرسِ = after the lesson
• أثناءَ الاجتماعِ = during the meeting

That is why المباراة takes the genitive ending in full MSA pronunciation.

Yes. That is also correct.

Compare:

• يبدو المدرب مشغولا قبل المباراة
• المدرب يبدو مشغولا قبل المباراة

Both mean the same thing: The coach seems busy before the match.

The difference is mostly one of word order and style:

• يبدو المدرب... = more naturally verbal, very standard in formal Arabic
• المدرب يبدو... = starts with the topic/subject, a bit closer to English order

A learner should be comfortable with both.

A careful full reading would be:

يَبْدُو المُدَرِّبُ مَشْغُولًا قَبْلَ المُبَارَاةِ

Transliteration:

yabdu l-mudarribu mashghūlan qabla l-mubārāti

A few useful notes:

• المدربُ is nominative as the subject
• مشغولًا is accusative
• المباراةِ is genitive after قبل

In less formal pronunciation, many speakers reduce or omit case endings, but in full MSA grammar they are there.