Mi ne povis mem levi la pezan ŝrankon, do du najbarinoj helpis min porti ĝin al la ĉambro.

Because povi means to be able / can, and in Esperanto it is used with an infinitive.

So:

• Mi ne povis = I could not / I was not able
• levi = to lift

Together, Mi ne povis levi... means I could not lift...

This works like English could lift or was able to lift.

Mem means by oneself, personally, or oneself for emphasis.

So Mi ne povis mem levi... means something like:

• I couldn't lift it by myself
• I myself couldn't lift it

Here it emphasizes that the speaker could not do it alone.

It is not quite the same as English reflexive myself in every situation, but in this sentence by myself is a very natural translation.

Because ŝrankon is the direct object, and Esperanto marks direct objects with -n.

• ŝranko = a cupboard / wardrobe / cabinet
• ŝrankon = the cupboard, as the thing being lifted

Adjectives must agree with the nouns they describe, so:

• peza ŝranko = a heavy cupboard
• pezan ŝrankon = a heavy cupboard, as a direct object

So both words take the endings that match:

• -a for adjective
• -n for accusative

Esperanto uses la only when the noun is definite, like English the.

So:

• pezan ŝrankon = a heavy cupboard
• la pezan ŝrankon = the heavy cupboard

In this sentence, the speaker is just introducing the object, not necessarily referring to one already known to the listener, so no la is needed.

Whether English uses a or the can depend on context, and Esperanto works similarly with la.

They are related, but not the same.

• levi = to lift, to raise
• porti = to carry

So the sentence says:

• the speaker could not lift the heavy cupboard alone
• two neighbors helped the speaker carry it to the room

This makes sense physically: first you lift something, then you carry or move it somewhere.

Because -in- is the Esperanto suffix for female.

• najbaro = neighbor
• najbarino = female neighbor
• najbarinoj = female neighbors

The -j marks plural.

So du najbarinoj means two female neighbors.

If you just wanted two neighbors without specifically saying they were female, you would normally say du najbaroj.

With helpi, Esperanto often uses the person helped as a direct object.

So:

• helpi iun fari ion = to help someone do something

That gives:

• helpis min porti ĝin = helped me carry it

This is a very common structure in Esperanto.

You may also see helpi al iu, but helpi iun is extremely common and usually the most natural pattern for learners to recognize first.

Both are accusative pronouns, because each is a direct object in its own clause.

• min = me
• ĝin = it

In du najbarinoj helpis min, min is the person being helped.

In porti ĝin, ĝin is the thing being carried, referring back to la/that cupboard mentioned earlier as ŝrankon.

So:

• helpis min = helped me
• porti ĝin = carry it

Because once the object has already been mentioned, Esperanto usually uses a pronoun just like English does.

So instead of saying:

• ...helpis min porti la ŝrankon...

the sentence says:

• ...helpis min porti ĝin...

That is more natural and avoids repetition.
Ĝin clearly refers back to the cupboard.

Because al already shows direction: to, toward.

In Esperanto, if a noun already has a preposition like al, you normally do not add the accusative -n just for movement.

So:

• al la ĉambro = to the room

Using -n here would generally be unnecessary and wrong in normal usage.

Compare:

• Mi iris al la ĉambro. = I went to the room.
• Mi eniris la ĉambron. = I entered the room.

In the second example, there is no preposition, so -n marks the goal/direction.

Do means so, therefore, or thus.

It connects the two parts of the sentence:

• Mi ne povis mem levi la pezan ŝrankon = I couldn't lift the heavy cupboard by myself
• do du najbarinoj helpis min... = so two female neighbors helped me...

It shows result or consequence.

Yes. Esperanto word order is fairly flexible, although some orders sound more natural than others.

The given order is very normal:

• Mi ne povis mem levi la pezan ŝrankon

It puts the negative ne before the verb povis, which is standard, and mem near the idea it emphasizes.

You could also see slightly different emphasis in sentences like:

• Mi mem ne povis levi la pezan ŝrankon.
  = I myself could not lift the heavy cupboard.

That puts stronger emphasis on I.

So the chosen word order is natural and emphasizes that the speaker could not do it alone.

A useful way to break it apart is:

• du najbarinoj = two female neighbors
• helpis min = helped me
• porti ĝin = to carry it
• al la ĉambro = to the room

So the pattern is:

[subject] + helpis + [person] + [infinitive phrase]

That means:

Two female neighbors helped me carry it to the room.

This is a very common Esperanto structure, and once you recognize it, sentences like this become much easier to read.