Jeg mangler hjælp med opgaven.

Because hjælp is usually treated as an uncountable noun here, like help in English.

So Danish says:

• Jeg mangler hjælp = I need help / I am lacking help

You would normally not say en hjælp in this sentence.

If you want to talk about a helper / an assistant, Danish would usually use a different noun, such as en hjælper.

Mangler is the present tense of at mangle.

In this sentence, at mangle means to lack, to be short of, or very often in natural English, to need.

So:

• Jeg mangler hjælp literally = I lack help
• natural English = I need help

This verb is very common in Danish for saying that something is missing or needed.

Examples:

• Jeg mangler penge. = I need money / I’m short of money.
• Vi mangler tid. = We need more time / We’re short on time.

Because the subject is jeg and the sentence is in the present tense.

In Danish, verbs do not change much depending on the person. The present tense is usually the same for all subjects.

So:

• jeg mangler
• du mangler
• han/hun mangler
• vi mangler

That is much simpler than English, where verbs sometimes change, like I need but he needs.

Opgaven is the definite singular form of opgave, which means task, assignment, or exercise, depending on context.

So:

• en opgave = a task / an assignment
• opgaven = the task / the assignment

In Danish, the definite article is often added to the end of the noun instead of being a separate word.

So instead of saying the assignment with a separate word like English does, Danish often says:

• opgaven = assignment-the

Med means with, so hjælp med opgaven means help with the assignment.

This is the natural preposition in Danish here, just as in English:

• help with the assignment
• hjælp med opgaven

If you used another preposition, the meaning could change or sound less natural.

Yes, absolutely.

Jeg har brug for hjælp med opgaven is another very natural way to say the same thing. It literally means I have use for help with the assignment, but in normal English it is simply I need help with the assignment.

Compare:

• Jeg mangler hjælp med opgaven.
• Jeg har brug for hjælp med opgaven.

Both are correct and natural.
A learner will often hear both.

Very roughly:

• mangler can sound a bit more like I’m lacking / I’m short of
• har brug for is a very direct need

No, and this is an important distinction.

• at mangle = to lack / to need / to be missing
• at savne = to miss in the emotional sense

So:

• Jeg mangler hjælp. = I need help.
• Jeg savner dig. = I miss you.

English uses miss for both ideas sometimes, but Danish usually keeps them separate.

This is standard Danish main-clause word order:

• Subject + verb + rest of sentence

So:

• Jeg = subject
• mangler = verb
• hjælp med opgaven = object/complement

Danish is a V2 language, which means the finite verb is usually in the second position in main clauses.

In this sentence, the subject comes first, so the verb comes right after it.

If you move something else to the front, the verb still stays second:

• Med opgaven mangler jeg hjælp.

That version is possible, but less neutral.

You normally put ikke after the verb phrase in a sentence like this:

• Jeg mangler ikke hjælp med opgaven. = I don’t need help with the assignment.

So the negative word ikke comes after mangler, not before it.

In a yes/no question, Danish usually puts the verb first:

• Mangler du hjælp med opgaven? = Do you need help with the assignment?

Notice that mangler comes before du.

You could also ask more directly:

• Har du brug for hjælp med opgaven?

Both are natural.

This is a word many learners notice because the spelling looks tricky.

A useful beginner approximation is something like hyelp, said as one syllable.

A few points:

• hj is not pronounced like a full English h + j
• the word is one syllable
• the æ sound is somewhat like the vowel in English cat, but not exactly

You do not need a perfect pronunciation immediately; this is a word Danes hear often, so context usually helps a lot.