Mi hermano quiere colgar un estante, pero no encuentra el taladro.

Because mi is the possessive adjective used before a noun:

• mi hermano = my brother
• mi casa = my house

Mío / mía / míos / mías are usually possessive pronouns or used after the noun for emphasis:

• El hermano es mío = The brother is mine
• un amigo mío = a friend of mine

So before hermano, you need mi.

Both are third-person singular present tense forms:

• quiere = he/she wants
• encuentra = he/she finds
• with no, no encuentra = he/she doesn’t find / can’t find

Here they refer to mi hermano, so:

• Mi hermano quiere... = My brother wants...
• ...pero no encuentra... = ...but he can’t find...

Spanish often leaves out the subject pronoun él because the verb ending already shows who the subject is.

After querer (to want), Spanish normally uses an infinitive:

• quiere colgar = wants to hang
• quiero comer = I want to eat
• queremos salir = we want to go out

So the pattern is:

• querer + infinitive

That is why colgar stays in the infinitive form.

Yes. Both are stem-changing verbs in the present tense.

• querer: e → ie
  • quiero, quieres, quiere, quieren
• encontrar: o → ue
  • encuentro, encuentras, encuentra, encuentran

So:

• quiere comes from querer
• encuentra comes from encontrar

This is very common in Spanish. The stem changes in most present-tense forms, but not usually in nosotros and vosotros:

• queremos
• encontramos

Colgar means to hang or to put up by hanging/suspending.

In this sentence, colgar un estante means something like:

• to hang/put up a shelf

In everyday English, you might naturally say put up a shelf, even if Spanish uses colgar.

A related note: colgar can also mean:

• to hang clothes
• to hang a picture
• to hang up the phone

So its meaning depends on context.

This is about the difference between the indefinite article and the definite article.

• un estante = a shelf
• el taladro = the drill

Why?

• un estante introduces it as just a shelf, not a specific one already identified.
• el taladro suggests a specific drill that the speaker and listener both know about, probably the one in the house/toolbox.

This works a lot like English:

• He wants to hang a shelf
• but he can’t find the drill

In Spanish, no normally goes directly before the conjugated verb:

• no encuentra = doesn’t find / can’t find
• no quiere = doesn’t want
• no tengo = I don’t have

So in this sentence:

• pero no encuentra el taladro

not:

• pero encuentra no...

That would be incorrect.

Encontrar means to find.

So:

• no encuentra el taladro = he can’t find the drill

If you want to say to look for, the verb is buscar:

• Busca el taladro = He is looking for the drill
• No encuentra el taladro = He can’t find the drill

English sometimes uses can’t find where the person is obviously also looking for something, so learners often confuse these two verbs.

Pero is the normal word for but when you are contrasting two ideas:

• quiere colgar un estante, pero no encuentra el taladro
• he wants to hang a shelf, but he can’t find the drill

Sino is used in a different kind of contrast, usually after a negative, when you correct or replace an idea:

• No es un martillo, sino un taladro = It’s not a hammer, but rather a drill

So in this sentence, pero is the correct choice.

Spanish often drops subject pronouns because the verb ending already tells you who the subject is.

• Mi hermano quiere... already makes it clear that the subject is my brother
• ...no encuentra... still refers to the same subject

You could say Él no encuentra el taladro, but it is usually unnecessary unless you want emphasis or contrast.

This is very normal in Spanish and much more common than in English.

Usually, yes. Taladro normally refers to a drill, especially the tool used to make holes in walls, wood, etc.

In this context, because he wants to put up a shelf, el taladro is naturally understood as the drill needed for the job.

In Spain, this is the standard word you would expect in this context.

A very close translation is:

• My brother wants to hang a shelf, but he can’t find the drill.

A slightly more natural everyday English version might be:

• My brother wants to put up a shelf, but he can’t find the drill.

That is useful to know because Spanish and English do not always choose the exact same verb, even when the meaning is the same.

Yes, depending on context, estante usually means shelf, but it can sometimes refer to a shelving unit or part of one.

Still, in this sentence, the most natural meaning is simply:

• estante = shelf

Learners should also know that estantería often means:

• bookcase
• shelving
• set of shelves

So estante is usually one shelf, while estantería is more like the whole shelving structure.