No podemos relacionar estos dos hechos.

In Spanish, standard negation usually goes directly before the conjugated verb.

So:

No podemos relacionar... = We cannot / can’t relate...

That is the normal pattern: no + conjugated verb

For example: No entiendo. = I don’t understand.
No quieren venir. = They don’t want to come.

If you said Podemos no relacionar..., that would mean something different: We can choose not to relate... So the position of no matters.

Because poder is a modal verb, like can in English. After poder, Spanish normally uses an infinitive.

So:

podemos relacionar = we can relate / connect

Not: podemos relacionamos or podemos relacionamos — those would be incorrect here.

This same pattern appears with other verbs too: Quiero comer. = I want to eat.
Debemos salir. = We must leave.
Pueden venir. = They can come.

Yes, poder is irregular, but only in certain forms.

Its stem changes from o to ue when the syllable is stressed:

puedo, puedes, puede, pueden

But in the nosotros and vosotros forms, the stem does not change:

podemos, podéis

So: yo puedo
tú puedes
él/ella puede
nosotros podemos
vosotros podéis
ellos pueden

That is why podemos is correct, not puedemos.

Good question. Spanish often uses relacionar A con B when the two things are named separately:

No podemos relacionar este hecho con el otro.
= We can’t relate this fact to the other one.

But when both items are treated together as one direct object, Spanish can simply say:

relacionar estos dos hechos

So No podemos relacionar estos dos hechos is completely natural. It means we cannot connect those two facts/events to each other.

Here, yes: it means to connect, to link, or to associate.

But you should be careful, because English relate has several meanings, and Spanish does not always use relacionar for all of them.

In this sentence: relacionar = connect/link

But if English relate means to tell or to recount, Spanish would usually use: relatar or contar

And if English relate to someone means identify with them, Spanish would more naturally use something like: identificarse con

So in this sentence, relacionar is specifically about making a connection between two things.

Not here. In this sentence, hechos is a noun, the plural of hecho.

un hecho can mean:

• a fact
• an event
• sometimes a deed

So estos dos hechos means these two facts/events.

It is true that hecho is also the past participle of hacer: He hecho la tarea. = I have done the homework.

But in estos dos hechos, it is clearly a noun, because it is being used with a demonstrative and a number: estos dos hechos

That structure shows it is not a participle here.

Because the personal a is mainly used with people (and sometimes pets or personified beings) when they are direct objects.

For example: Veo a María. = I see María.

But hechos are things, not people, so there is no personal a:

No podemos relacionar estos dos hechos.

That is exactly what we expect.

Because estos is a demonstrative adjective, and in Spanish demonstratives normally replace the article rather than combine with it.

So: estos hechos = these facts

Not: los estos hechos = incorrect in normal Spanish

The usual order is:

demonstrative + number + noun

So: estos dos hechos

That is the natural way to say these two facts/events.

Spanish demonstratives show distance or perspective.

Very roughly: estos = these, near the speaker / close in the discourse
esos = those, a bit farther away / often near the listener or less close
aquellos = those over there / more distant

In many real contexts, especially in modern speech, the distinctions are not always very strict. Here, estos often suggests the two facts we are currently talking about.

So it feels natural if the speaker has just mentioned them or is focusing on them directly.

Yes. That is also correct, but the focus changes a little.

No podemos relacionar estos dos hechos
= We can’t relate these two facts.

No se pueden relacionar estos dos hechos
= These two facts can’t be related / connected
or
= One cannot relate these two facts

The version with podemos sounds more personal: we cannot do it.

The version with se pueden sounds more impersonal or general, as if the problem is not about us specifically but about whether the connection is possible at all.

In standard Peninsular Spanish, approximately:

No podemos relacionar estos dos hechos
[no po-DE-mos re-la-thyo-NAR ES-tos dos E-chos]

A few useful notes:

• h in hechos is silent.
• ch sounds like the ch in church.
• In most of Spain, the c before i in relacionar is pronounced like th in thin.
• podemos has the stress on de.
• relacionar has the stress on the last syllable: -nar.

So: podemos → poDEmos
relacionar → relacionAR
hechos → HEchos

If you hear Latin American Spanish, relacionar will usually have an s sound there instead of the Peninsular th sound.