Jeg kigger på baghjulet igen, før jeg går til værkstedet.

Because at kigge på means to look at something.

• Jeg kigger = I’m looking / I’m glancing
• Jeg kigger på baghjulet = I’m looking at the rear wheel

In Danish, many verbs need a preposition where English does too, and kigge på is a very common combination.

Baghjulet is a compound noun:

• bag- = rear / back
• hjul = wheel
• baghjul = rear wheel
• baghjulet = the rear wheel

Danish very often joins nouns into one word, much more than English does. So where English says rear wheel, Danish often makes a compound: baghjul.

The -et is the definite ending, meaning the.

So:

• et baghjul = a rear wheel
• baghjulet = the rear wheel

This is very common in Danish. Instead of putting a separate word like the in front, Danish usually adds the definite ending to the noun.

For the same reason as with baghjulet: Danish usually marks definiteness with an ending on the noun.

• et værksted = a workshop / garage
• værkstedet = the workshop / garage

So til værkstedet means to the workshop/garage, even though there is no separate word like English the.

Igen means again.

In this sentence:

• Jeg kigger på baghjulet igen = I look at the rear wheel again

Its placement is natural after the object here. Danish word order with adverbs can vary a bit depending on style and emphasis, but this position is very common and sounds natural.

Because før introduces a subordinate clause: before I go to the workshop.

In Danish subordinate clauses, the normal order is usually:

conjunction + subject + verb

So:

• før jeg går til værkstedet

not

• før går jeg til værkstedet

The version with går jeg would be the kind of inversion you see in a main clause, not after før.

Yes, går literally means walks, but in Danish it is also often used in the broader sense of goes, especially in everyday language.

So jeg går til værkstedet can mean:

• I’m going to the workshop
• and in some contexts it may suggest going on foot, but not always strongly

If you wanted to be more neutral about transportation, you might sometimes use tager til or another verb depending on context, but går til is perfectly normal.

Danish often uses the present tense for near-future or planned actions, just like English often does.

So:

• før jeg går til værkstedet literally looks like before I go to the workshop
• but it can refer to something that is about to happen or is planned

This is completely normal Danish usage.

Til means to here and marks movement toward a place.

• gå til værkstedet = go to the workshop
• køre til værkstedet = drive to the workshop

So til is the natural preposition with movement toward a destination.

Yes, absolutely. That is a very natural alternative.

Compare:

• Jeg kigger på baghjulet igen, før jeg går til værkstedet.
• Før jeg går til værkstedet, kigger jeg på baghjulet igen.

They mean the same thing, but the emphasis shifts a little.

Also notice the word order change in the second version: when the subordinate clause comes first, the main clause has inversion:

• ... kigger jeg ...

not

• ... jeg kigger ...

That is a very important Danish word-order rule.

Not always. It depends on context.

Værksted can mean:

• workshop
• garage
• repair shop
• mechanic’s shop

In this sentence, because it mentions a rear wheel, many learners would understand værkstedet as something like the garage or the repair shop. The exact English word depends on the situation.