Honum mistókst að klára millifærsluna, því PIN-númerið var ekki rétt.

Because the verb mistakast uses the person who experiences the failure in the dative case, not the nominative.

So:

• hann = he / nominative
• honum = him / dative

A very common pattern is:

• Mér mistókst ... = I failed to ...
• Honum mistókst ... = He failed to ...

Literally, it is closer to It failed for him than to the English structure He failed.

Mistókst is the past tense of mistakast, which means to fail, to not succeed, or to go wrong.

In this sentence:

• Honum mistókst að klára millifærsluna
  = He failed to finish the transfer

This verb is very common when talking about unsuccessful attempts.

A useful pattern to remember is:

• e-m mistókst að + infinitive

where e-m means someone in the dative case.

Examples:

• Mér mistókst að hringja. = I failed to call.
• Henni mistókst að opna hurðina. = She failed to open the door.

Because að + infinitive is the normal way to say to + verb in Icelandic.

So:

• að klára = to finish
• að fara = to go
• að sjá = to see

After mistakast, Icelandic often uses this structure:

• Honum mistókst að klára ...
• literally: To him failed to finish ...
• natural English: He failed to finish ...

Millifærsluna is the accusative singular definite form of millifærsla.

Breakdown:

• millifærsla = a transfer / bank transfer
• millifærslu = accusative singular
• millifærsluna = the transfer (accusative singular definite)

It is accusative because it is the direct object of klára:

• klára hvað? = finish what?
• millifærsluna = the transfer

So the sentence is talking about a specific transfer, not just any transfer.

Here því means because.

So:

• ..., því PIN-númerið var ekki rétt.
• ..., because the PIN number was not correct.

You may also see því að, which means the same thing:

• því að = because
• því = because

In many modern sentences, að is simply left out.

In Icelandic, when an abbreviation or acronym is combined with another noun, a hyphen is often used.

So:

• PIN-númer = PIN number
• PIN-númerið = the PIN number

The definite article is added to the whole compound at the end:

• númer = number
• númerið = the number

This is a very normal Icelandic spelling pattern with abbreviations.

Because númer is a neuter noun, and PIN-númerið is the definite singular form.

Breakdown:

• PIN-númer = a PIN number
• PIN-númerið = the PIN number

In the second clause, this word is the subject of var:

• PIN-númerið var ekki rétt
• The PIN number was not correct

Since it is neuter singular, other words connected to it also appear in neuter singular form.

Because rétt is agreeing with PIN-númerið, which is neuter singular.

The adjective réttur changes form depending on gender, number, and case:

• réttur = masculine
• rétt = neuter
• rétt can also appear in some feminine/case combinations, but here it is specifically neuter singular

Since the subject is PIN-númerið (neuter singular), Icelandic uses:

• PIN-númerið var rétt = The PIN number was correct
• PIN-númerið var ekki rétt = The PIN number was not correct

This is predicate adjective agreement after vera (to be).

Because in Icelandic, ekki normally comes after the finite verb.

So:

• var ekki rétt = was not correct

This is the standard placement in a simple clause:

• Hann kemur ekki. = He is not coming.
• Það var ekki gott. = That was not good.
• PIN-númerið var ekki rétt. = The PIN number was not correct.

English uses not, while Icelandic uses ekki, but the word order is not always exactly the same.

Yes.

• vera = to be
• er = is
• var = was

So:

• PIN-númerið er rétt. = The PIN number is correct.
• PIN-númerið var rétt. = The PIN number was correct.

In your sentence:

• var ekki rétt = was not correct

Yes, and that is actually a very helpful way to understand the grammar.

A more literal view is:

• Honum mistókst að klára millifærsluna
• To him, it failed to finish the transfer

That is not natural English, but it shows why Icelandic uses the dative (honum) instead of a normal nominative subject like hann.

So the best natural translation is still:

• He failed to finish the transfer

But the literal idea helps explain the structure.