Tom hangt een plank aan de muur met een hamer en een paar spijkers.

Because the subject is Tom, which is third person singular.

The infinitive is hangen = to hang.
In the present tense:

• ik hang
• jij hangt
• hij/zij/het hangt
• wij/jullie/zij hangen

So Tom hangt means Tom hangs / is hanging / hangs up.

Also note that in normal pronunciation, hangt is often said a bit like hangt with the ngt cluster compressed.

Aan de muur means on the wall in the sense of attached to the wall.

Dutch often uses aan where English uses on for something that is hanging or fixed to a vertical surface.

So:

• aan de muur = on the wall / attached to the wall
• op de muur would usually sound odd here, because op is more like on top of or on the surface of in a different way

For pictures, shelves, boards, mirrors, etc., aan de muur is very common.

That is about articles:

• een = a/an
• de = the for most Dutch nouns
• het = the for neuter nouns

So:

• een plank = a board / a shelf
• de muur = the wall

In this sentence, the plank is being introduced as new information, so the indefinite article een is natural. The wall is treated as a specific wall, so de muur is used.

Also, muur is a de-word, so the definite article is de.

Yes, plank literally means plank or board, but in context it can also mean a shelf, especially if you are attaching it to a wall.

So depending on context, een plank aan de muur hangen may be understood as:

• hanging a board on the wall
• putting up a shelf

Dutch often leaves that slightly broad unless the speaker wants to be more specific.

It describes the means or tools Tom is using.

So the structure is basically:

• Tom = subject
• hangt = verb
• een plank = direct object
• aan de muur = location/result
• met een hamer en een paar spijkers = with a hammer and a few nails

In other words, Tom is using a hammer and nails to attach the plank to the wall.

English speakers sometimes wonder whether this could attach to de muur, but in normal interpretation it clearly describes how Tom does it.

Usually, een paar means a few or a couple of, not necessarily exactly two.

So:

• een paar spijkers = a few nails

If you want to be clearly exact, Dutch can use:

• twee spijkers = two nails

In everyday Dutch, een paar is often approximate.

Yes, Dutch word order is flexible, especially with extra information like place, time, or means.

This sentence has a very natural order:

Tom hangt een plank aan de muur met een hamer en een paar spijkers.

A common way to think about it is:

• subject
• finite verb
• object
• place
• means/instrument

But Dutch can move things around for emphasis. For example:

Tom hangt met een hamer en een paar spijkers een plank aan de muur.

That is also possible, and it puts more focus on the tools.

So the original sentence is normal, but not the only possible order.

Both can be possible, depending on nuance.

• hangen can mean to hang or to put something so that it hangs
• ophangen often means to hang up

So:

• Tom hangt een plank aan de muur = Tom hangs/puts a plank on the wall
• Tom hangt een plank aan de muur op is possible in some contexts, but often sounds heavier or more emphatic

In simple everyday descriptions, hangen is fine here.

That said, Dutch learners should know that ophangen is very common with things like:

• een jas ophangen = hang up a coat
• een schilderij ophangen = hang up a painting

It is understandable and grammatical, but there is a small practical nuance: people usually hang up things like pictures, while a plank attached with nails might also be described with verbs like bevestigen or monteren if you want to sound more technical.

Still, the sentence is perfectly normal for learning purposes, and native speakers will understand it easily.

The phrase met een hamer en een paar spijkers also helps make the action very clear.

Dutch uses prepositions differently from English.

Here, aan already carries the idea of attachment/location relative to the wall. So Dutch does not need a separate word matching English to.

That is why:

• aan de muur can correspond to on the wall
• in this context, with the verb, the whole phrase helps express the result of attaching something to the wall

So you should learn aan de muur as a natural Dutch expression, not translate it word-for-word.

Een plank is the direct object.

It is the thing Tom is hanging.

So:

• Tom = subject, the person doing the action
• hangt = verb
• een plank = direct object, the thing affected by the action

That is why the sentence means Tom is doing something to the plank, not that Tom himself is hanging.

A careful pronunciation would be roughly:

Tom hangt een plank aan de muur met een hamer en een paar spijkers.

A few useful sound notes:

• hangt: the ngt cluster is compact; the g is not strongly separate for many speakers
• plank: the a is short
• muur: long uu sound, somewhat like a rounded long vowel not found in standard English
• hamer: stress on the first syllable
• spijkers: ij is the Dutch ij/ei sound, somewhat like the vowel in English time, though not exactly

If you are reading it aloud, the main stress will usually fall on content words like Tom, plank, muur, hamer, and spijkers.