Attól függően, hogy homályos-e a kép, másik sort olvasok.

It means depending on whether or more literally depending on the fact of whether.

This is a very common Hungarian pattern:

• attól függően = depending on that
• hogy... = introduces the clause that explains what it depends on

So:

• Attól függően, hogy homályos-e a kép... = Depending on whether the picture/image is blurry...

It is a more formal, more structured way to say something than a simple if clause.

Because the verb függ means depend, and in Hungarian it normally takes the ending -tól / -től on the thing depended on:

• függ valamitől = depend on something

So:

• attól = from that / on that
• függően = depending

Together, attól függően is a fixed expression meaning depending on that.

The attól points forward to the clause introduced by hogy. English does this differently, but Hungarian often uses this kind of forward-pointing structure.

That is a very common learner question.

Yes, hogy often means that, but in this structure it introduces an embedded yes/no clause, so in English it is best translated as whether.

Here the clue is -e in homályos-e:

• hogy homályos-e a kép = whether the image is blurry

So in this sentence:

• hogy is introducing the clause
• -e marks it as a yes/no question inside the sentence

That is why the whole part means whether the picture is blurry, not just that the picture is blurry.

The suffix -e marks a yes/no question, especially in embedded or more formal language.

So:

• A kép homályos. = The picture is blurry.
• Homályos-e a kép? = Is the picture blurry?
• hogy homályos-e a kép = whether the picture is blurry

In your sentence, it is not a direct question to another person. It is an embedded question inside a larger sentence, so English uses whether.

Because in Hungarian, the verb to be is often omitted in the present tense, third person when the predicate is a noun or adjective.

So:

• A kép homályos. literally looks like The picture blurry but it means The picture is blurry

This is normal Hungarian grammar.

That is why the question form is:

• homályos-e a kép

and not something with an explicit present-tense is.

Both kinds of order can exist, but the version in your sentence is very natural in this type of embedded whether clause.

Hungarian word order is flexible and often depends on focus and information structure. Here, putting homályos-e first makes the blurry or not part feel central.

Compare:

• A kép homályos. = neutral statement
• homályos-e a kép = whether the picture is blurry

So this order works well after hogy in a clause like this.

Because sort is the accusative form of sor.

• sor = line / row
• sort = line / row as a direct object

Since olvasok means I read, the thing being read must be in the accusative:

• másik sort olvasok = I read another/different line

The -t marks the direct object.

This is about the Hungarian indefinite vs definite conjugation.

Hungarian uses:

• indefinite conjugation when the object is indefinite or non-specific
• definite conjugation when the object is definite and specific

Here:

• másik sort = another/a different line
• this is treated as indefinite
• so the verb is olvasok

If the object were definite, you would use the definite form:

• A másik sort olvasom. = I am reading the other line.

So:

• másik sort olvasok = indefinite
• a másik sort olvasom = definite

Másik usually means another, the other, or a different one, depending on context.

In this sentence, it most naturally means:

• another line
• a different line

It suggests switching from one line to another one.

This is slightly different from más, which more generally means other / different.
Másik often feels more like choosing a different item from a set.

Because Hungarian normally leaves out subject pronouns when the verb ending already shows the person.

• olvasok = I read / I am reading

The ending -ok already tells you the subject is I, so én is unnecessary unless you want emphasis.

For example:

• Én olvasok másik sort. would sound like I am the one reading another line, with extra emphasis on I.

In your sentence, the neutral form without én is the normal choice.

Yes, you could, but it is not exactly the same in tone.

• Ha homályos a kép, másik sort olvasok. = If the picture is blurry, I read another line.

• Attól függően, hogy homályos-e a kép, másik sort olvasok. = Depending on whether the picture is blurry, I read another line.

The ha version is a straightforward condition.
The attól függően, hogy version emphasizes that your action varies according to the condition. It sounds a bit more formal and more explicitly dependent on that factor.

It can mean either, depending on context.

• In reading text, sor often means line
• In a chart, table, or test sheet, it may mean row

So másik sort olvasok could mean:

• I read another line
• I read a different row

The correct English choice depends on the situation.