אני בקושי שומעת אותך, כי המזגן ממש רועש.

שומעת is the feminine singular present-tense form of לשמוע (to hear).

So this sentence is being said by a female speaker:

• אני בקושי שומעת אותך

If the speaker were male, it would be:

• אני בקושי שומע אותך

The form tells you about the speaker’s gender, not the listener’s.

בקושי means barely, hardly, or with difficulty.

In this sentence, אני בקושי שומעת אותך means:

• I can barely hear you
• literally, something like I barely hear you

It often gives the idea that something is only happening a little, or is very difficult to do.

Hebrew often does not use a separate verb for can in sentences like this.

English says:

• I can barely hear you

Hebrew naturally says:

• I barely hear you

The idea of ability is understood from the context. If you wanted to sound more explicit, you could also say something like:

• אני לא מצליחה לשמוע אותך — I’m not managing to hear you
• אני כמעט לא שומעת אותך — I almost don’t hear you / I can hardly hear you

But אני בקושי שומעת אותך is very natural.

אותך is the direct object form of you.

Since לשמוע (to hear) takes a direct object, Hebrew uses אותך:

• שומעת אותך — hear you

This is different from the subject form אתה / את (you).

A useful thing to know: in normal unpointed writing, אותך can represent:

• אוֹתְךָ (otkha) — you masculine
• אוֹתָךְ (otakh) — you feminine

So the spelling here does not tell you whether the listener is male or female.

Yes, often it can.

Because שומעת already shows first person singular feminine, Hebrew can drop the pronoun if the subject is clear:

• בקושי שומעת אותך, כי המזגן ממש רועש.

That sounds natural in conversation.

Including אני makes the sentence a little more explicit, and it is also very normal. Hebrew often includes subject pronouns even when they are not strictly necessary.

מזגן means air conditioner.

The ה־ at the beginning is the, so:

• מזגן — air conditioner
• המזגן — the air conditioner

Also, מזגן is a masculine singular noun, which matters for agreement later in the sentence.

In present-tense Hebrew, the verb to be is usually omitted.

So:

• המזגן ממש רועש

literally looks like:

• the air conditioner really noisy

but it means:

• the air conditioner is really noisy

In the past or future, Hebrew does use forms of to be, for example:

• המזגן היה רועש — the air conditioner was noisy
• המזגן יהיה רועש — the air conditioner will be noisy

Because רועש agrees with המזגן, and מזגן is masculine singular.

So:

• מזגן רועש — a noisy air conditioner / the air conditioner is noisy

If the noun were feminine singular, you would use רועשת:

• מכונה רועשת — a noisy machine

Hebrew adjectives and predicate adjectives must agree in gender and number.

In Hebrew, adjectives normally come after the noun.

For example:

• מזגן רועש — a noisy air conditioner

In your sentence, רועש is functioning as a predicate adjective:

• המזגן ממש רועש — the air conditioner is really noisy

So even though English uses is in the middle, Hebrew still places the adjective after the noun.

ממש is an intensifier. It means really, very, or truly, depending on context.

So:

• רועש — noisy
• ממש רועש — really noisy

It is extremely common in spoken Hebrew and sounds very natural here.

Yes. כי is a very common and standard way to say because.

So:

• כי המזגן ממש רועש — because the air conditioner is really noisy

Another common option in spoken Hebrew is בגלל ש־, but כי is simpler and very natural in this sentence.

The dictionary form is לשמוע, meaning to hear.

The present-tense forms are:

• שומע — masculine singular
• שומעת — feminine singular
• שומעים — masculine plural / mixed plural
• שומעות — feminine plural

So שומעת is the feminine singular present form built from לשמוע.