Ne tiru tiun tirkeston tro forte, ĉar ĝi povas rompiĝi.

Tiru is the -u form, which Esperanto uses for commands, requests, and exhortations.

• tiras = pulls / is pulling
• tiru = pull! / do pull / should pull

Because the sentence is telling someone not to do something, Esperanto uses:

• Ne tiru = Don’t pull

So Ne tiras would not work here for a command.

In Esperanto, commands often leave out the subject because it is understood.

• (Vi) ne tiru = Don’t pull

You can include vi if you want, but normally it is omitted because the listener is obvious.

Because tiu is part of the direct object, it takes the accusative ending -n.

• tiu = that
• tiun = that one / that, as a direct object

Here, the thing being pulled is that drawer, so Esperanto marks it with -n:

• tiun tirkeston

For the same reason: it is the direct object of tiru.

You are pulling the drawer, so tirkesto gets -n:

• tirkesto = drawer
• tirkeston = drawer, as the direct object

Both tiun and tirkeston take -n because they belong to the same noun phrase.

Tirkesto is a compound word:

• tir- from tiri = to pull
• kesto = box, chest, case

So tirkesto literally means something like pull-box, which is Esperanto’s normal word for drawer.

This is very typical Esperanto word-building.

Because the sentence needs an adverb, not an adjective.

• forta = strong
• forte = strongly

The word is describing how someone pulls:

• tiru ... forte = pull ... strongly / hard

In Esperanto, adverbs usually end in -e.

Tro means too in the sense of excessively.

So:

• forte = strongly / hard
• tro forte = too hard / too strongly

It shows that the action goes beyond a safe or reasonable amount.

Ĉar means because. It introduces the reason for the command.

So the structure is:

• Ne tiru ..., ĉar ...
• Don’t pull ..., because ...

It connects the warning to its explanation.

Ĝi refers to tiu tirkesto — the drawer.

In Esperanto, ĝi is the normal pronoun for a thing or an animal when sex is not being specified.

So here:

• ĝi povas rompiĝi = it can break

with it meaning the drawer.

This is a very important Esperanto point.

• rompi = to break something
• rompiĝi = to break / get broken on its own, or to become broken

Examples:

• Mi rompis la glason. = I broke the glass.
• La glaso rompiĝis. = The glass broke.

So in your sentence:

• ĝi povas rompiĝi = it may break / it can get broken

The ending -iĝ- often shows a change of state, not a reflexive meaning like break itself in English.

Because povas adds the idea of possibility.

• rompiĝas = is breaking / breaks
• povas rompiĝi = can break / might break

The sentence is not saying the drawer is already breaking. It says pulling it too hard creates the possibility that it will break.

In this sentence, it is closer to might or may in natural English.

Literally, povas means can, but with things like this it often expresses possibility:

• ĝi povas rompiĝi = it can break
• more naturally in English: it might break

So the idea is not that the drawer has the skill to break, but that breaking is a real possibility.

Yes, Esperanto word order is fairly flexible, but this version is the most natural and clear.

Standard order here is:

• command: Ne tiru tiun tirkeston tro forte
• reason: ĉar ĝi povas rompiĝi

You might move some parts for emphasis, but for a learner, this sentence is a very good normal model to follow.