Attól függően, hogy melyikkel látok jobban, az optikus segít választani.

It is a fixed expression meaning depending on.

• attól = on that / from that
• függően comes from függ = to depend

So attól függően introduces the basis or condition for something else: depending on ...

They are related, but not used in quite the same way.

• Attól függ, hogy... = It depends on whether/how...
• Attól függően, hogy... = Depending on whether/how...

So attól függ, hogy... can be the main statement by itself, while attól függően, hogy... works more like an introductory phrase attached to another clause.

In your sentence, the main clause is az optikus segít választani.

Because hogy introduces the subordinate clause that explains what the dependence is based on.

So:

• attól függően = depending on
• hogy melyikkel látok jobban = which one I see better with

This pattern is very common in Hungarian: attól függően, hogy...

Melyik means which one.

Here it has the instrumental/comitative ending -val / -vel, which often means with. So:

• melyik = which one
• melyikkel = with which one

In context, it means something like with which one or through which one, probably referring to lenses, glasses, or options the optician is showing.

Because of a very common sound/spelling change with -val / -vel.

When this suffix is added to a word ending in a consonant, the v often assimilates to the final consonant, and that consonant gets doubled in spelling.

So:

• melyik + vel becomes melyikkel

The same kind of thing happens in words like:

• kéz + vel → kézzel
• ablak + val → ablakkal

Because Hungarian uses indefinite and definite verb conjugation, and here there is no definite direct object.

• látok = indefinite
• látom = definite

In this sentence, melyikkel is not a direct object. It means with which one, so it is an instrumental phrase, not the thing being directly seen. That is why látok is correct.

Because jobban is the adverb form, and it modifies the verb látok.

• jobb = better as an adjective
• jobban = better as an adverb

So:

• jobb szemüveg = better glasses
• jobban látok = I see better

Since the sentence is talking about how I see, Hungarian uses jobban.

Literally, it means the optician helps to choose.

Hungarian often uses:

• segít + infinitive

So:

• segít választani = helps choose / helps to choose

In natural English, you would usually say the optician helps me choose.

It is omitted because Hungarian often leaves out things that are clear from context.

So az optikus segít választani can naturally mean:

• the optician helps me choose
• or more literally, the optician helps with choosing

If you wanted to say me explicitly, you could add nekem:

• Az optikus segít nekem választani.

Because Hungarian often omits the object if it is obvious from the situation.

Here, the missing object is probably something like:

• glasses
• lenses
• frames
• the better option

So segít választani is perfectly natural when both speakers already know what is being chosen.

Because Hungarian word order is flexible, and the first part often gives the background, condition, or frame for the main statement.

So this order:

• Attól függően, hogy melyikkel látok jobban, az optikus segít választani.

puts the condition first: depending on which one I see better with...

That is a very natural way to structure the sentence.

Because az optikus means the optician, a specific one known in the situation.

• az optikus = the optician
• egy optikus = an optician / a certain optician

In this sentence, it sounds like the speaker is talking about the optician they are currently dealing with, so az optikus is the natural choice.