בלי המרשם הזה אני לא יכולה לקנות את התרופה לשיעול.

בלי means without.

So בלי המרשם הזה means without this prescription.

It is a very common preposition in Hebrew, and it is followed directly by the thing that is missing:

• בלי כסף = without money
• בלי עזרה = without help
• בלי המרשם הזה = without this prescription

In Hebrew, demonstratives such as הזה and הזאת usually come after the noun, not before it.

So:

• המרשם הזה = this prescription
• literally: the prescription this

This is normal Hebrew word order.

The prefix ה־ is the Hebrew definite article, meaning the.

So:

• מרשם = prescription
• המרשם = the prescription
• תרופה = medicine
• התרופה = the medicine

In המרשם הזה, the noun is definite because Hebrew normally says the X this, not just X this.

Hebrew often expresses can / be able to with יכול / יכולה plus an infinitive.

Here:

• אני לא יכולה = I cannot / I am not able
• לקנות = to buy

So אני לא יכולה לקנות literally means I am not able to buy, which is the normal way to say I can’t buy.

Because the speaker is female.

In the present tense, יכול / יכולה agrees with the gender and number of the subject:

• אני יכול = I can, said by a male
• אני יכולה = I can, said by a female

So this sentence is being said by a woman or girl.

In Hebrew, לא normally comes before the verb or predicate that it negates.

So:

• אני יכולה = I can
• אני לא יכולה = I cannot

Putting לא before יכולה is the standard way to make the sentence negative.

לקנות is the infinitive to buy.

In Hebrew, infinitives usually begin with ל־, which often corresponds to English to:

• לקנות = to buy
• לראות = to see
• ללכת = to go

After יכול / יכולה, Hebrew normally uses an infinitive:

• יכולה לקנות = can buy

את is the marker of a definite direct object.

It usually does not get translated into English, but it appears before a direct object that is definite, such as one with ה־.

So:

• לקנות תרופה = to buy medicine / a medicine
• לקנות את התרופה = to buy the medicine

Because התרופה is definite, Hebrew uses את before it.

לשיעול means for cough or for a cough, depending on context.

Here:

• ל־ = for
• שיעול = cough

So תרופה לשיעול is literally medicine for cough, which in natural English is cough medicine or medicine for a cough.

Sometimes yes, especially in conversation, if the subject is already clear from context.

You might hear:

• לא יכולה לקנות את התרופה לשיעול בלי המרשם הזה

However, in the present tense, forms like יכולה can mean I, you, or she depending on context, so keeping אני makes the sentence clearer.

That is why אני is very natural here.

Yes.

The sentence you have puts בלי המרשם הזה first for emphasis:

• בלי המרשם הזה אני לא יכולה לקנות את התרופה לשיעול.

A more neutral order would be:

• אני לא יכולה לקנות את התרופה לשיעול בלי המרשם הזה.

Both are correct. The version with בלי המרשם הזה first highlights the missing prescription right away.

Only יכולה would change to יכול:

• בלי המרשם הזה אני לא יכול לקנות את התרופה לשיעול.

Everything else stays the same.

A simple transliteration is:

Bli ha-mirsham ha-ze ani lo yekhola liknot et ha-trufa le-shi'ul.

Approximate stress:

• bli
• ha-mirSHAM
• ha-ZE
• a-NI
• lo
• yekho-LA
• lik-NOT
• et
• ha-tru-FA
• le-shi-UL

Transliterations can vary a little, but this should help you read it aloud.