Mekanikeren siger, at nummerpladen sidder løst, men at bilen ellers ser fin ud.

Because -en is the usual definite ending for a singular common-gender noun in Danish.

• mekaniker = a mechanic
• mekanikeren = the mechanic

The same thing happens elsewhere in the sentence:

• nummerplade → nummerpladen = the license plate
• bil → bilen = the car

Unlike English, Danish usually adds definiteness to the end of the noun instead of using a separate word like the.

Because the sentence contains two coordinated that-clauses, both depending on siger.

Structure:

• Mekanikeren siger
  • at nummerpladen sidder løst
  • men at bilen ellers ser fin ud

In English, you might say:

• The mechanic says that the license plate is loose, but that the car otherwise looks fine
• or more naturally: ...but the car otherwise looks fine

English often drops the second that, but Danish commonly keeps the second at to make the structure clear and balanced.

Because after at, Danish uses subordinate clause word order.

In a main clause, Danish usually has verb-second word order:

• Bilen ser ellers fin ud

But in a subordinate clause introduced by at, the subject normally comes before the finite verb, and sentence adverbs like ellers come before that verb:

• at bilen ellers ser fin ud

So:

• main clause: Bilen ser ellers fin ud
• subordinate clause: at bilen ellers ser fin ud

This is one of the most important word-order differences in Danish.

Right—sidde is used much more broadly in Danish than sit is in English.

Here, sidder means something like:

• is attached
• is positioned
• is sitting in place

So nummerpladen sidder løst means the license plate is loosely attached or not firmly fixed.

Danish often uses sidde for things that are mounted, fastened, or located somewhere:

• Skiltet sidder på døren = The sign is on the door
• Knappen sidder løst = The button is loose

Because in this kind of expression, Danish often uses the -t form to describe how something is positioned or attached.

So:

• løs = loose
• løst = the form commonly used in expressions like sidder løst

This happens especially after verbs such as:

• sidde
• hænge
• stå
• ligge

Examples:

• Skruen sidder løst = The screw is loose
• Billedet hænger skævt = The picture is hanging crooked

So løst here is the normal form in this construction.

Here ellers means otherwise, apart from that, or in other respects.

So:

• bilen ellers ser fin ud = the car otherwise looks fine
• in natural English: the car looks fine apart from that

It signals that there is one problem—the loose license plate—but aside from that, things seem okay.

It is built from the verb se ... ud, which means to look or to appear.

So:

• ser ud = looks / appears
• ser fin ud = looks fine

The word ud is part of the verbal expression. Danish often uses these verb + particle combinations, and the particle may appear later in the clause.

Examples:

• Hun ser træt ud = She looks tired
• Det ser godt ud = It looks good
• Bilen ser fin ud = The car looks fine

So ud is not optional here; it helps create the meaning look/appear.

Because ser fin ud is a bit more cautious and observational.

• er fin = is fine
• ser fin ud = looks fine / appears fine

A mechanic often judges based on inspection, so ser fin ud sounds natural: the car seems to be in good shape, at least from what can be seen.

This difference is similar to English:

• The car is fine = stronger, more definite
• The car looks fine = what it seems like

Here fin means something like:

• fine
• okay
• in good shape
• all right

It does not mainly mean pretty here. In the context of a mechanic talking about a car, fin is an everyday way of saying the car seems to be in good condition overall.

So bilen ser fin ud means something like:

• the car looks fine
• the car otherwise seems okay

There are two separate things going on:

1. The comma before men is normal, because men joins two clauses.
2. The comma before the first at depends on Danish comma style.

In modern Danish, some writers use a comma before subordinate clauses like at nummerpladen sidder løst, while others leave it out, depending on whether they use start comma or not.

So you may see both:

• Mekanikeren siger, at nummerpladen sidder løst, men at bilen ellers ser fin ud.
• Mekanikeren siger at nummerpladen sidder løst, men at bilen ellers ser fin ud.

Both can be acceptable, depending on the comma system being followed. The comma before men is the less optional one.