Geturðu útskýrt hvaða forsetningu ég á að nota með þessu orði?

Yes. Geturðu is basically getur þú with þú reduced and attached to the verb.

This is very common in spoken Icelandic and also in normal informal-to-neutral writing, especially in direct questions:

• Geturðu komið? = Can you come?
• Viltu hjálpa? = Do you want to help?

So Geturðu sounds very natural. Getur þú is also possible, but it can sound a bit more careful, formal, or emphatic.

Because after geta in this kind of sentence, Icelandic normally uses the form called the supine:

• geta útskýrt
• geta sagt
• geta hjálpað

So Geturðu útskýrt ...? is the normal pattern.

This is different from some other verbs. For example:

• Ég vil útskýra = I want to explain
• Ég get útskýrt = I can explain

So this is a pattern worth memorizing: geta + supine.

Because geta does not take að before the next verb in this construction.

So you say:

• Geturðu útskýrt ...?

not:

• Geturðu að útskýra ...?

That is just how this verb works. A learner often has to memorize which verbs are followed by að + infinitive, which take no að, and which take another non-finite form.

It can be either, depending on context.

In hvaða forsetningu, it means something like:

• which preposition
• or what preposition

English often uses either one here. Icelandic hvaða is the normal word used before a noun when asking this kind of question.

So:

• hvaða forsetningu = which/what preposition

Because hvaða is the form used before a noun.

Compare:

• Hvað er þetta? = What is this?
• Hvaða bók viltu? = Which/what book do you want?
• Hvaða forsetningu ... = Which/what preposition ...

So hvað usually stands alone, while hvaða comes before a noun.

That is a very common question. Hvaða is indeclinable, so it stays the same regardless of gender, number, or case.

So the case is shown by the noun, not by hvaða:

• hvaða forsetning
• hvaða forsetningu
• hvaða orð
• hvaða orði

In this sentence, the important case ending appears on forsetningu, not on hvaða.

The dictionary form is forsetning = preposition.

Here it appears as forsetningu, which is the accusative singular form. That is because it is the object of nota in the embedded clause:

• ég á að nota hvaða forsetningu
  = I am supposed to use which preposition

So the basic idea is:

• forsetning = base form
• forsetningu = object form used here

This is the very common construction eiga að + infinitive, which usually means:

• to be supposed to
• should
• ought to

So:

• ég á að nota = I should use / I am supposed to use

This does not mean I own to use. Even though eiga by itself can mean own, in this construction it has a different meaning.

Compare:

• Ég á bíl. = I own a car.
• Ég á að fara. = I am supposed to go.

Because this is an embedded question, not a main question.

In the main clause, Icelandic uses question word order:

• Geturðu útskýrt ...?

But inside the clause introduced by hvaða, Icelandic uses normal statement-like word order:

• hvaða forsetningu ég á að nota

This is similar to English:

• Which preposition should I use?
  but
• Can you explain which preposition I should use?

So once the question is embedded, the subject ég comes before the verb á.

Because með takes the dative.

So both words are in the dative singular:

• þessu = dative of þessi/þetta
• orði = dative of orð

The base form is:

• þetta orð = this word

But after með, it becomes:

• með þessu orði = with this word

So this part is a good example of case agreement:

• the demonstrative changes
• the noun changes
• both match each other in case, number, and gender

Because the sentence is asking about which preposition, not referring to a specific already-known preposition.

In Icelandic, the is usually added as a suffix to the noun:

• forsetning = a preposition / preposition
• forsetningin = the preposition
• forsetninguna = the preposition in the accusative

So hvaða forsetningu is the natural indefinite form for which preposition.

You can add fyrir mér.

A natural version would be:

• Geturðu útskýrt fyrir mér hvaða forsetningu ég á að nota með þessu orði?

That means:

• Can you explain to me which preposition I should use with this word?

The original sentence simply leaves to me unstated, because it is not necessary.

A quick guide:

• þ is like th in thing
• ð is like th in this

So:

• þessu starts with the thing sound
• Geturðu has a soft ð, often very light in normal speech
• hvaða also contains ð

Also, modern Icelandic hv is often pronounced roughly like kv, so hvaða may sound closer to kvaða than an English learner might expect from the spelling.