Ég spurði lyfjafræðinginn hvort þetta lyf gæti valdið höfuðverk.

Spurði is the past tense of spyrja, which means to ask.

• Ég spyr = I ask / I am asking
• Ég spurði = I asked

So the sentence is talking about something that already happened.

The ending -inn is the suffixed definite article, so lyfjafræðinginn means the pharmacist.

The basic noun is:

• lyfjafræðingur = pharmacist

After the verb spyrja in this kind of sentence, the person being asked is in the accusative case:

• lyfjafræðing = a pharmacist
• lyfjafræðinginn = the pharmacist

So Ég spurði lyfjafræðinginn means I asked the pharmacist.

Here hvort means whether.

It introduces an indirect yes/no question:

• Ég spurði ... hvort ... = I asked ... whether ...

English often uses if in this kind of sentence, but in Icelandic hvort is the normal word for whether in reported questions like this.

This is a very common question because English uses if for two different jobs.

In Icelandic, they are usually separated:

• hvort = whether in indirect questions
• ef = if in conditions

So:

• Ég spurði hvort þetta lyf gæti valdið höfuðverk.
  = I asked whether this medicine could cause a headache.

But:

• Ef þú tekur þetta lyf, verðurðu syfjaður.
  = If you take this medicine, you will get sleepy.

So in your sentence, hvort is correct because it is not a condition; it is an indirect question.

Because þetta already works as the determiner this, so you normally do not also add the definite article to the noun.

• þetta lyf = this medicine
• lyfið = the medicine

Using both together would usually be wrong here. Icelandic generally does not stack this/that together with the suffixed article the way English learners might expect.

Gæti is a form of geta that often means could / might.

In this sentence, it fits because the speaker is reporting a question about possibility:

• getur = can
• gæti = could / might

So:

• Getur þetta lyf valdið höfuðverk?
  = Can this medicine cause a headache?

becomes, in indirect form:

• Ég spurði hvort þetta lyf gæti valdið höfuðverk.
  = I asked whether this medicine could cause a headache.

This use of gæti also sounds natural in reported or less certain statements.

Formally, gæti is historically a past subjunctive form, but in everyday meaning here it does not simply mean past time.

In this sentence, it mainly expresses possibility or uncertainty, much like English could.

So it is better to think of it here as a modal form meaning:

• could
• might

rather than as a straightforward past tense.

The verb valda means to cause, and it takes the dative case.

The noun is:

• höfuðverkur = headache

After valda, it appears in the dative:

• valda höfuðverk = cause a headache / cause headache

For this noun, the dative singular happens to look the same as the accusative singular, so you just see höfuðverk.

This is worth memorizing because many Icelandic verbs require a specific case, and valda is one of the classic dative verbs.

Icelandic does not have an indefinite article like English a/an.

So a bare noun can often mean:

• a headache
• headache
• sometimes a more general idea depending on context

That is why höfuðverk on its own can naturally correspond to English a headache in this sentence.

Because this is an indirect question, not a direct one.

Direct question:

• Getur þetta lyf valdið höfuðverk?
  = Can this medicine cause a headache?

Indirect question:

• Ég spurði hvort þetta lyf gæti valdið höfuðverk.
  = I asked whether this medicine could cause a headache.

In the indirect version, Icelandic uses subordinate clause word order, so the subject þetta lyf comes before gæti.

Here it is singular: this medicine.

You can tell from þetta, which is neuter singular here.

A tricky thing is that lyf can look the same in singular and plural in some forms, so learners often have to rely on the determiner or the context.

In this sentence:

• þetta lyf = this medicine

not these medicines.

Yes, that is also grammatical.

The difference is:

• þetta lyf = this medicine
• lyfið = the medicine

So þetta lyf points to a specific medicine more directly, often one that is physically present or just mentioned. Lyfið simply means the medicine, assuming it is already understood which one you mean.

Both are natural, but þetta lyf is especially useful when you mean this particular medicine.

A few parts are especially tricky for English speakers:

• þ in þetta is like th in think
• ð in valdið is like th in this, though in Icelandic it can sound weaker depending on position
• hvort is usually pronounced with an initial sound close to kv
• æ in gæti is pronounced like i in English fine, so gæti is roughly like GUY-ti, though not exactly
• ll is not present here, but Icelandic double consonants often need special attention in general

A rough learner-friendly approximation of some words would be:

• þetta ≈ THET-ta
• hvort ≈ kvort
• gæti ≈ GUY-ti

These are only approximations, but they can help you get started.