אנחנו יכולים להרכיב את המדף לבד.

יכולים is the masculine plural form of יכול (can / able to).

Because the subject is אנחנו (we), the adjective-like form after it has to agree in number and usually also in gender:

• אנחנו יכולים = we can (for a group of males or a mixed group)
• אנחנו יכולות = we can (for an all-female group)

So this sentence is either talking about a male group or a mixed group.

Here, יכולים means can or are able to.

Hebrew often uses forms of יכול to express ability:

• אני יכול = I can
• את יכולה = you can
• אנחנו יכולים = we can

So אנחנו יכולים להרכיב... literally means we are able to assemble..., which is the normal way to say we can assemble...

להרכיב is the infinitive, meaning to assemble / to put together.

After יכול / יכולים, Hebrew normally uses an infinitive:

• יכול ללכת = can go
• יכולים לעשות = can do
• יכולים להרכיב = can assemble

The ל־ at the beginning is part of the infinitive form, like to in English.

In this sentence, להרכיב means to assemble, to put together, or to mount.

It is a very natural verb for furniture, devices, or anything made of parts. So if you are talking about building a shelf from pieces, להרכיב is exactly the kind of verb Hebrew uses.

את marks a definite direct object.

It does not really get translated into English, but it appears before a direct object when that object is definite, for example:

• את הספר = the book
• את הילד = the boy
• את המדף = the shelf

Here, המדף is definite because of ה־ (the), so Hebrew requires את:

• אנחנו יכולים להרכיב את המדף = We can assemble the shelf

If the object were indefinite, you would usually not use את:

• אנחנו יכולים להרכיב מדף = We can assemble a shelf

מדף means shelf.

Adding ה־ to the beginning makes it the shelf:

• מדף = a shelf / shelf
• המדף = the shelf

So in the sentence:

• את המדף = the shelf

לבד means alone, by ourselves, or on our own, depending on context.

In this sentence, since the subject is we, לבד is naturally understood as:

• by ourselves
• on our own

So the sentence suggests that we can assemble the shelf without help.

Putting לבד at the end is very natural in Hebrew.

Hebrew word order is fairly flexible, but this order sounds normal and clear:

• אנחנו יכולים להרכיב את המדף לבד

It is similar to English putting alone or by ourselves near the end:

• We can assemble the shelf ourselves
• We can assemble the shelf alone

The final position makes לבד feel like an added detail about how we can do it.

Yes. בעצמנו means ourselves / by ourselves, and it is often even more explicit than לבד.

Compare:

• אנחנו יכולים להרכיב את המדף לבד = We can assemble the shelf alone / by ourselves
• אנחנו יכולים להרכיב את המדף בעצמנו = We can assemble the shelf ourselves

Both are natural.
בעצמנו puts a little more emphasis on we ourselves, while לבד can sound slightly more like without anyone else.

In this sentence, אנחנו is very helpful and usually natural.

In Hebrew present tense, forms like יכולים show gender and number, but not clearly person the way English does. So יכולים by itself could mean something like:

• they can
• you can
• we can

depending on context.

Because of that, speakers often include the pronoun:

• אנחנו יכולים... = we can...

So yes, אנחנו is useful here for clarity.

Usually, יכולים here is understood as ability, not formal permission.

So the most natural reading is:

• We are able to assemble the shelf by ourselves
• We can assemble the shelf ourselves

In some contexts, English can can mean permission, but in Hebrew, if you want to be clearly about permission, you might use something like:

• מותר לנו להרכיב את המדף לבד = We are allowed to assemble the shelf by ourselves

So יכולים most naturally means are able to.

Then יכולים would become יכולות:

• אנחנו יכולות להרכיב את המדף לבד.

Everything else stays the same.

So:

• אנחנו יכולים = we can (male or mixed group)
• אנחנו יכולות = we can (all-female group)

A common pronunciation would be:

anákhnu yekholím leharkív et hamadáf levád

A more fully pointed version is:

אֲנַחְנוּ יְכוֹלִים לְהַרְכִּיב אֶת הַמָּדָף לְבַד

Very roughly word by word:

• אנחנו = anákhnu
• יכולים = yekholím
• להרכיב = leharkív
• את = et
• המדף = hamadáf
• לבד = levád

Hebrew can move things around more than English, but the original order is the most straightforward and natural:

• אנחנו יכולים להרכיב את המדף לבד.

You may hear variations for emphasis, but they can sound marked or context-dependent. For a learner, the original order is the best model:

subject + can + infinitive + object + adverb

So this sentence is a very good standard pattern to remember.