У сына сломалась точилка, и он не смог заточить карандаш.

Russian very often uses у + Genitive to show possession or the person affected by something.

So У сына сломалась точилка is literally something like At the son, the sharpener broke, but in natural English it means The son's sharpener broke or His son’s sharpener broke.

This pattern is extremely common in Russian:

• У меня есть книга = I have a book
• У брата машина = My brother has a car
• У сына сломалась точилка = The son's sharpener broke

It is often more natural in Russian than trying to build a possessive phrase the way English does.

Because the preposition у requires the Genitive case.

The dictionary form is сын.
Its Genitive singular is сына.

So:

• сын = son
• у сына = of the son / at the son / the son has

This is just standard case government: у + Genitive.

Because the subject is точилка, and точилка is a feminine singular noun.

In the past tense, Russian verbs agree with gender and number:

• masculine: сломался
• feminine: сломалась
• neuter: сломалось
• plural: сломались

Since точилка is feminine, the verb must be сломалась.

Here it is part of the verb сломаться, which means to break, to become broken, or to break down.

Compare:

• сломать = to break something
• сломаться = to break, to become broken

So:

• Он сломал точилку = He broke the sharpener
• Точилка сломалась = The sharpener broke

In this sentence, nobody is directly said to have broken it; the sentence just states that it ended up broken. That is why сломаться is used.

Because сломала is from сломать, which is a transitive verb: it means broke something.

For example:

• Она сломала точилку = She broke the sharpener

But in your sentence, точилка itself is the thing that became broken, so Russian uses the intransitive/reflexive form:

• Точилка сломалась = The sharpener broke

So the difference is:

• сломала = someone broke something
• сломалась = something broke

Russian often drops personal pronouns when the subject is obvious, but in the past tense the verb does not show person as clearly as in the present tense.

Here, after У сына сломалась точилка, adding он makes it clear that the next action refers to the son, not to someone else.

So и он не смог заточить карандаш clearly means and he couldn’t sharpen the pencil.

Without он, the sentence could still sometimes be understood from context, but including it makes the reference much clearer and more natural here.

Смочь is the perfective partner of мочь.

• мочь = to be able, can
• смочь = to manage to, to succeed in being able to

So:

• не мог often describes a state or ongoing inability: could not / was unable
• не смог often means did not manage to on this specific occasion

In this sentence, there is a specific event: the sharpener broke, and as a result, he was not able to complete the action. That is why не смог fits very well.

So the nuance is roughly:

• не мог заточить = he could not sharpen it
• не смог заточить = he failed to manage to sharpen it

Both can be possible in some contexts, but не смог sounds especially natural for a single completed situation.

Because заточить is perfective, and it focuses on the completed result: getting the pencil sharpened.

Compare:

• точить = to sharpen, to be sharpening, to do the process
• заточить = to sharpen completely / to get sharpened

After смог / не смог, Russian often uses a perfective infinitive when the idea is whether the action was successfully completed.

So:

• не смог заточить карандаш = he couldn’t sharpen the pencil
  meaning he failed to get it sharpened

If you said не смог точить карандаш, it would sound less natural here and would focus more on the process itself rather than the completed result.

It is in the Accusative, but for masculine inanimate nouns in the singular, the Accusative looks the same as the Nominative.

So:

• Nominative: карандаш
• Accusative: карандаш

That is why the form does not change.

Compare with an animate masculine noun:

• я вижу брата = I see my brother

Here the Accusative matches the Genitive because брат is animate.

But карандаш is inanimate, so the Accusative stays the same as the dictionary form.

Точилка means sharpener, usually a pencil sharpener.

It comes from the verb точить, meaning to sharpen.

So the word family is helpful:

• точить = to sharpen
• заточить = to sharpen fully
• точилка = sharpener

In this sentence, точилка is the tool he would use to sharpen the pencil.

The meaning stays basically the same if you change the word order, but the emphasis can shift.

For example:

• У сына сломалась точилка puts early focus on the son / his situation
• Точилка у сына сломалась puts early focus on the sharpener

Russian word order is more flexible than English, and it often reflects what is already known and what is being emphasized.

The given order sounds very natural if you are introducing the son as the affected person first: As for the son, his sharpener broke.