Frater fatetur se verbum “possum” bene coniugare non posse, sed conari.

The main clause is Frater fatetur = The brother admits.

Everything after that is what he admits: se verbum possum bene coniugare non posse, sed conari.

So the structure is roughly:

• Frater = subject
• fatetur = main verb
• se ... non posse, sed conari = indirect statement, telling us what he admits

Inside that indirect statement, coniugare goes with posse: to be able to conjugate.

Because fateor is a deponent verb.

Deponent verbs use passive-looking forms, but they have active meanings. So:

• fatetur looks like a passive form
• but it actually means he admits or he confesses

Its dictionary form is fateor, fateri, fassus sum.

Latin often does not use a separate word for that in this kind of sentence.

After verbs like say, think, know, hear, admit, and similar verbs, Latin usually uses an accusative-and-infinitive construction instead of a clause with that.

So English says:

• He admits that he cannot...

But Latin says, more literally:

• He admits himself not to be able...

That is why you get se ... non posse instead of a clause introduced by that.

Se is the accusative subject of the indirect statement.

After fatetur, Latin puts the subject of the reported statement in the accusative. Here that subject is the same person as the main subject, so Latin uses the reflexive pronoun se.

So:

• Frater fatetur se... = The brother admits that he...

If it referred to someone else, Latin might use eum instead.

They are infinitives because they belong to the indirect statement after fatetur.

In this construction, Latin normally uses:

• an accusative subject: se
• one or more infinitives: posse, conari

So:

• se ... non posse = that he is not able
• sed conari = but that he is trying

Also, conari is the infinitive of another deponent verb, conor, so it too looks passive but has an active meaning: to try.

Because possum means be able, and it usually takes another infinitive to complete the idea.

So:

• posse = to be able
• coniugare = to conjugate

Together, coniugare posse means to be able to conjugate.

With the negative, coniugare non posse means not to be able to conjugate.

Because what is being denied is the ability.

So coniugare non posse means not to be able to conjugate.

That is slightly different from negating coniugare by itself. Latin word order is flexible, but here the sense is clearly that he lacks the ability, not that he is able but somehow does not conjugate.

In other words, the idea is:

• he cannot conjugate it well not
• he is able not to conjugate it well

Because Latin often leaves repeated words understood.

Once se has already been given as the subject of the infinitives, it can continue to be understood with the next infinitive:

• se ... non posse, sed conari
• literally: himself ... not to be able, but to try

Latin does this kind of omission very naturally. English usually has to fill it out more explicitly: that he cannot..., but is trying.

Here possum is being mentioned as a word or verb-form, not used in its normal meaning.

So verbum possum means something like:

• the word possum
• or, in grammatical English, the verb possum

This is a metalinguistic use: the sentence is talking about the word itself.

Also, verbum can mean word in general, and in grammatical contexts it can also be used when talking about a verb.

Because when you mention a Latin word, you can cite the exact form you want to talk about.

Here the speaker is referring to the verb under the name possum, which is a familiar dictionary form and the first-person singular present form.

So verbum possum means the word or verb possum as an item of language. It does not mean that the sentence is suddenly switching to first person.

The form posse later in the sentence is different: there it is an infinitive actually functioning grammatically in the sentence.

Bene modifies coniugare.

So the sense is to conjugate well.

That whole phrase then belongs with posse:

• bene coniugare non posse = not to be able to conjugate well

Latin adverbs can move around fairly freely, so the placement may not match English exactly, but the connection here is clear.