אם את עייפה, אני יכול להציע לך קפה חם.

In the present tense, Hebrew usually leaves out the verb to be.

So את עייפה literally looks like you tired, but it means you are tired.

This is completely normal Hebrew.
Compare:

• אני עייף = I am tired
• היא שמחה = She is happy

If you want past or future, Hebrew does use forms of to be:

• היית עייפה = you were tired
• תהיי עייפה = you will be tired

Both את and עייפה show that the person being addressed is female singular.

• את = you when speaking to one woman/girl
• עייפה = tired in the feminine singular form

Hebrew often marks gender, so the adjective has to match the person it describes.

If you were speaking to a man, you would say:

אם אתה עייף, אני יכול להציע לך קפה חם.

Because יכול agrees with the speaker, not with the listener.

In this sentence:

• את עייפה = the listener is female
• אני יכול = the speaker is male

So the full idea is: If you (female) are tired, I (male) can offer you hot coffee.

If the speaker were female, she would say:

אני יכולה להציע לך קפה חם.

אם means if and introduces a condition.

So:

אם את עייפה = if you are tired

Hebrew does not need a separate word for then in this kind of sentence. English can say If you are tired, then I can offer you hot coffee, but Hebrew usually just says:

אם את עייפה, אני יכול...

You can add אז sometimes for emphasis, but it is not necessary.

להציע is the infinitive, meaning to offer or sometimes to suggest, depending on context.

The ל־ at the beginning is the normal marker used in many Hebrew infinitives, similar to English to in to offer.

So:

• יכול להציע = can offer
• literally: can to-offer

This is a normal structure in Hebrew after words like יכול.

לך means to you or for you.

In this sentence, it marks the person receiving the offer:

• להציע לך = to offer you

It is made from the preposition ל־ meaning to/for plus a pronoun.

A useful thing to know: in unpointed Hebrew, לך is spelled the same for masculine and feminine singular, but the pronunciation differs:

• to a woman: lach
• to a man: lecha

Here, because the sentence is addressing a woman, it is understood as lach.

Hebrew has the but not a separate word for a/an.

So:

• קפה can mean coffee or a coffee, depending on context
• הקפה means the coffee

That is why קפה חם can naturally mean hot coffee or a hot coffee.

This is very common in Hebrew and usually feels natural once you get used to it.

In Hebrew, adjectives usually come after the noun.

So:

• קפה חם = hot coffee
• literally: coffee hot

Also, the adjective must match the noun in gender and number.

קפה is masculine singular, so the adjective is also masculine singular: חם.

For comparison:

• משקה קר = cold drink
• עוגה חמה = hot cake / warm cake
  Here חמה is feminine because עוגה is feminine.

Several words may change, because Hebrew marks gender.

Here are the main possibilities:

• male speaker -> female listener
  אם את עייפה, אני יכול להציע לך קפה חם.

• female speaker -> female listener
  אם את עייפה, אני יכולה להציע לך קפה חם.

• male speaker -> male listener
  אם אתה עייף, אני יכול להציע לך קפה חם.

• female speaker -> male listener
  אם אתה עייף, אני יכולה להציע לך קפה חם.

The main things that change are:

• את / אתה
• עייפה / עייף
• יכול / יכולה

It is the same spelling, but it is not the same word.

In this sentence, את is the pronoun you for one female.

But Hebrew also has את as a grammatical marker used before a definite direct object, as in:

אני רואה את הספר. = I see the book.

These two את words are different in function, and traditionally they are pronounced differently when pointed:

• pronoun את = at
• object marker את = et

In normal unpointed writing, they look identical, so you understand them from context.

Yes, להציע can mean both to offer and to suggest, depending on context.

In this sentence, because the object is קפה חם, the most natural meaning is offer:

I can offer you hot coffee.

But in another sentence, it might clearly mean suggest, for example:

אני מציע ללכת הביתה. = I suggest going home.

So the exact English translation depends on what is being proposed.