אני לא יכולה לעשות שיעורי בית בלי דף.

Because the speaker is grammatically feminine singular.

In Hebrew, יכול/יכולה has to agree with the subject:

• אני לא יכולה... = said by a female speaker
• אני לא יכול... = said by a male speaker

So if a man were saying the same sentence, it would be:

אני לא יכול לעשות שיעורי בית בלי דף.

Because the sentence means cannot, so Hebrew negates the ability word:

• אני לא יכולה לעשות... = I cannot do...

This is different from:

• אני יכולה לא לעשות... = I can choose not to do...

So the position of לא changes the meaning.

Hebrew commonly uses יכול/יכולה + an infinitive to express can / be able to.

So:

• יכולה = can / am able
• לעשות = to do

Together:

• יכולה לעשות = can do

Also, the ל־ at the beginning of לעשות is part of the infinitive form, so לעשות already means to do.

Because את is only used before a definite direct object.

Here, שיעורי בית is being used in a general sense, like homework in English, not the homework. So no את is needed.

Compare:

• לעשות שיעורי בית = to do homework
• לעשות את שיעורי הבית = to do the homework

So if you make it definite, you would normally add both את and ה:

• אני לא יכולה לעשות את שיעורי הבית בלי דף.

Literally, it is something like home lessons or lessons of the house/home, but as a fixed expression it simply means homework.

This is a very common Hebrew phrase, and learners should usually just remember it as the standard way to say homework.

Because this is a construct phrase in Hebrew.

The basic plural noun is:

• שיעורים = lessons

But when it is followed by another noun to form a phrase like lessons of X, it changes into the construct form:

• שיעורי

So:

• שיעורים = lessons
• שיעורי בית = homework

This construct pattern is very common in Hebrew.

You would say:

שיעורי הבית

In Hebrew construct phrases, definiteness is usually shown on the second noun, and the whole phrase becomes definite.

So:

• שיעורי בית = homework / some homework / homework in general
• שיעורי הבית = the homework

That is why you do not usually say השיעורי בית.

Because בלי is the normal everyday word for without.

It is very common in both speech and writing:

• בלי מים = without water
• בלי דף = without a sheet/page

There is also ללא, which also means without, but it sounds more formal or written:

• ללא דף is possible, but less conversational.

דף usually means sheet, page, or leaf of paper.

So בלי דף most naturally means:

• without a sheet of paper
• without a page

If you specifically want to say paper as a material, Hebrew often uses:

• נייר = paper

So depending on the context:

• בלי דף = without a sheet/page
• בלי נייר = without paper

Because the sentence is talking about a sheet/page, not multiple sheets.

If you wanted to say without pages/sheets, you could use the plural:

• בלי דפים

But singular is perfectly natural if the idea is that one sheet is needed.

Usually not in this sentence, because יכולה by itself does not tell you the person clearly. It only shows feminine singular, so it could mean:

• I can
• you can (to a woman, in some contexts)
• she can

So אני is important here to make it clear that the subject is I.

This is the most neutral and natural order:

• אני = subject
• לא יכולה = cannot
• לעשות = do
• שיעורי בית = homework
• בלי דף = without a sheet/page

So the structure is basically:

subject + negation/ability + infinitive + object + prepositional phrase

Hebrew can sometimes move things around for emphasis, but this order is the standard one for a simple statement like this.