Learn Icelandic: Spyr læknirinn um ástæðu vandamálsins? - Does the doctor ask about the reason for the problem?

It is the genitive singular definite form of the neuter noun vandamál (problem). First, we add the standard genitive -s ending to get vandamáls. Then, we attach the definite article for the genitive neuter case, which is -ins, giving us vandamálsins (of the problem).

Why is there no word for "for" or "of" before vandamálsins?

In English, we say "the reason for the problem" or "the reason of the problem." In Icelandic, you simply place the second noun (vandamálsins) immediately after the first one and use the genitive case. The genitive case itself expresses this connection, so no extra preposition is needed.

Why is the word ástæðu used instead of its dictionary form ástæða?

The preposition um (about) forces the noun that directly follows it into the accusative case. Ástæða (reason) is a feminine noun, and its accusative singular form changes the ending to -u, making it ástæðu.

Why does the sentence start with the verb spyr?

Because this is a yes/no question. Icelandic forms yes/no questions by putting the verb first, followed immediately by the subject (læknirinn). English uses helping verbs like "does" for this, but Icelandic simply swaps the verb and subject.