Jeg holder øje med min søn på legepladsen.

Yes. At holde øje med is a common Danish idiom. It means to keep an eye on, to watch, or to keep track of someone or something.

It should usually be learned as one unit:

• holde øje med nogen = keep an eye on someone
• holde øje med noget = keep an eye on something

So in this sentence, holder øje med works like one verbal expression, not as three separately translated words.

No. Danish uses the singular in this idiom, just like English often does in keep an eye on.

So:

• holde øje med = correct
• holde øjne med = not correct here

Even though a person literally has two eyes, the expression is fixed in the singular.

Because med is part of the fixed expression holde øje med.

You cannot normally just say holde øje and then attach the object directly. The person or thing being watched comes after med:

• Jeg holder øje med min søn.
• Hun holder øje med trafikken.

So med is not optional here.

Holder is the present tense form of the verb at holde.

Danish verbs are not conjugated for person the way English verbs sometimes are, but they do change for tense:

• at holde = to hold / to keep
• holder = keep/keeps, am/is/are keeping
• holdt = kept

Since the sentence is a normal present-tense statement with jeg, Danish uses holder:

• Jeg holder øje med ... = I keep an eye on ...

Because sin/sit/sine is only used when the possessor refers to a third-person subject such as han, hun, or de.

Since the subject here is jeg, Danish uses min:

• Jeg holder øje med min søn. = I am watching my son.

Compare:

• Han holder øje med sin søn. = He is watching his own son.
• Han holder øje med hans søn. = He is watching someone else’s son.

So with jeg, du, vi, and I, you use the ordinary possessives like min, din, vores, jeres.

Because in Danish, a possessive normally replaces the article.

So you say:

• min søn = my son

not:

• min sønnen
• den min søn

This is similar to English: we say my son, not the my son.

Because Danish usually puts the definite article at the end of the noun.

So:

• en legeplads = a playground
• legepladsen = the playground

That -en is the definite ending. So på legepladsen means at/on the playground.

Danish often uses på for places understood as activity areas, surfaces, sites, or public locations. A playground is normally viewed that way, so på legepladsen is the natural choice.

• på legepladsen = at the playground / on the playground

Using i would usually sound less natural here, unless you were stressing being physically inside some enclosed space. In ordinary Danish, på legepladsen is what you would expect.

In normal interpretation, it describes the situation as a whole: the watching is happening at the playground, and the son is also understood to be there.

So the sentence naturally means:

• I am keeping an eye on my son at the playground.

Danish often leaves this kind of attachment slightly flexible, just like English does. Context usually makes it clear.

Yes. The sentence shown has the normal neutral order:

• Jeg holder øje med min søn på legepladsen.

But Danish is a verb-second language, so if you move another element to the front, the verb still stays in second position:

• På legepladsen holder jeg øje med min søn.

That version is also correct. It puts more focus on på legepladsen.

There is no exact English equivalent, which is why many learners ask about it.

A useful approximation:

• make a vowel like e in bed
• but round your lips as if saying o

That gives you something close to Danish ø.

Very roughly:

• øje sounds like OE-yeh
• søn has a short ø sound, something like suhn but with rounded lips and without using a normal English u

The exact sound is best learned by listening and imitating, but the key point is that ø is a separate vowel in Danish, not just an o or an e.