Δεν έχω μάθει ακόμα να φτιάχνω παζλ τόσο γρήγορα όσο ο γιος μου.

Δεν έχω μάθει means I haven’t learned / I haven’t learned how yet and focuses on the situation up to now.

• δεν έχω μάθει = I haven’t learned yet
• δεν έμαθα = I didn’t learn / I failed to learn (a past event)
• δεν μαθαίνω = I’m not learning / I don’t learn

So here Greek uses the present perfect to show that the skill has not been acquired yet.

Μάθει is the form used with έχω to build the modern Greek perfect:

• έχω μάθει = I have learned
• έχει μάθει = he/she has learned

It does not change for person; the person is shown by έχω, έχει, έχουμε, etc.

It happens to look like the form you also see after να in some contexts, but here its job is simply to help form the perfect tense.

Here ακόμα means yet.

So:

• Δεν έχω μάθει ακόμα = I haven’t learned yet

In other contexts, ακόμα can also mean still or even, depending on the sentence. Here, because the sentence is negative, yet is the natural meaning.

You may also see the spelling ακόμη. It means the same thing.

After μαθαίνω, Greek normally uses να + verb to mean learn to... / learn how to...

So:

• μαθαίνω να οδηγώ = I learn to drive
• μαθαίνω να μαγειρεύω = I learn to cook
• έχω μάθει να φτιάχνω παζλ = I have learned how to do puzzles

English uses to, but modern Greek does not have an infinitive like English. Instead, it uses να plus a verb form.

This is a question of aspect, which is very important in Greek.

• να φτιάχνω = imperfective aspect
• να φτιάξω = perfective aspect

Here, να φτιάχνω παζλ refers to a general skill or repeated activity: doing puzzles in general. That is why φτιάχνω is the natural choice.

If you said να φτιάξω, it would sound more like learning to complete one whole puzzle or a single finished action.

So in this sentence:

• να φτιάχνω παζλ = to be able to do/assemble puzzles as an activity

Literally, φτιάχνω often means make, but with παζλ it commonly means do, put together, or assemble a jigsaw puzzle.

So φτιάχνω παζλ is a normal Greek way to say:

• do puzzles
• put puzzles together
• assemble jigsaw puzzles

It does not usually mean create or invent puzzles here.

Here παζλ is being used generically, like puzzles in general, so no article is needed.

• φτιάχνω παζλ = I do puzzles
• φτιάχνω ένα παζλ = I’m doing a puzzle
• φτιάχνω το παζλ = I’m doing the puzzle

Also, παζλ is an indeclinable loanword, so its form usually stays the same. Context tells you whether it means a puzzle or puzzles in general.

In this sentence, it is best understood as puzzles / jigsaw puzzles as an activity.

Because the sentence needs an adverb, not an adjective.

• γρήγορος = fast, quick (adjective)
• γρήγορα = quickly, fast (adverb)

Here it describes how the action is done:

• φτιάχνω παζλ γρήγορα = I do puzzles quickly

So γρήγορα modifies the verb φτιάχνω.

τόσο ... όσο ... is the standard Greek pattern for as ... as ...

So:

• τόσο γρήγορα όσο ο γιος μου = as quickly as my son

Compare:

• τόσο μεγάλος όσο... = as big as...
• τόσο καλά όσο... = as well as...

If you wanted faster than my son, Greek would use a different pattern:

• πιο γρήγορα από τον γιο μου = faster than my son

So:

• τόσο ... όσο ... = as ... as ...
• πιο ... από ... = more ... than ...

Because ο γιος μου is understood as the subject of an omitted verb.

The full idea is:

• τόσο γρήγορα όσο ο γιος μου [φτιάχνει παζλ]
• as quickly as my son [does puzzles]

Since ο γιος μου is the subject of that implied verb, it stays in the nominative case:

• ο γιος μου = nominative
• τον γιο μου = accusative

So the nominative is correct here.

Yes. Greek often leaves out repeated material when it is obvious.

So this sentence really means something like:

• Δεν έχω μάθει ακόμα να φτιάχνω παζλ τόσο γρήγορα όσο ο γιος μου φτιάχνει παζλ.

But repeating φτιάχνει παζλ would sound heavy and unnecessary, so Greek leaves it out.

English does something similar:

• as quickly as my son
• or more fully, as quickly as my son does

Because in Greek, possessive expressions usually take the definite article:

• ο γιος μου = my son
• η κόρη της = her daughter
• το σπίτι μας = our house

So the article is not extra; it is just the normal Greek structure.

English says my son, but Greek normally says the son my in structure:

• ο γιος μου

Greek word order is fairly flexible, but this version is very natural.

A few things are especially normal here:

• δεν goes right before the finite verb: δεν έχω
• ακόμα sits near the idea of not yet
• the comparison comes at the end: τόσο γρήγορα όσο ο γιος μου

You could also hear:

• Ακόμα δεν έχω μάθει να φτιάχνω παζλ τόσο γρήγορα όσο ο γιος μου.

That has the same basic meaning, with a little more emphasis on still / yet at the beginning.