Post paucos dies puer quoque equitat, et equus eum bene portat.

Post is a preposition that (in this meaning) takes the accusative and means after.
So post paucos dies = after a few days.
Here paucos is accusative plural masculine agreeing with dies.

Dies here is accusative plural (because it follows post).
In the 5th declension, diēs is usually masculine (though it can be feminine in some contexts), so paucos is masculine to match it.

Pauci diēs would be nominative plural and would typically mean a few days as a subject (e.g., pauci diēs sunt = a few days exist/have passed).
But with post, you need the accusative: post paucos diēs.

Quoque means also / too and commonly comes after the word it emphasizes.
So puer quoque = the boy too / the boy also (i.e., in addition to someone else already mentioned).

Most naturally it means the boy also rides (the boy is an additional rider).
Because quoque is attached to puer, it highlights the boy as the “also”-element, not the riding itself.

Equitat is 3rd person singular present active indicative from equitāre = to ride (a horse).
In Latin, equitāre is typically intransitive: you “ride” without needing a direct object like a horse.

Eum is accusative singular masculine of is, ea, id = he / that person.
It refers back to puer (the boy). It’s used because portat needs a direct object: the horse carries him.

Bene is an adverb meaning well. It modifies portat: bene portat = carries well.
Adverbs are flexible in placement, but bene often appears right before (or sometimes after) the verb it modifies.

Both equitat and portat are present tense.
Latin often uses the present in narrative or descriptive passages to state what is happening as a general current action: the boy rides… the horse carries….

Latin can use pronouns, but it often repeats a noun for clarity or style, especially when switching subjects.
Here, repeating equus makes it immediately clear that the second clause’s subject is the horse.