Learn Danish: Kan du forklare hvorfor undersøgelsen er vigtig? - Can you explain why the investigation is important?

Because this is an indirect question, which acts as a subordinate clause. In a normal, direct question, the verb comes right after the question word (Hvorfor er undersøgelsen vigtig?). But when the question is embedded inside another sentence like after Kan du forklare, the subject (undersøgelsen) must come before the verb (er).

Why do we use the infinitive forklare instead of the present tense forklarer?

Because it comes right after the modal verb kan (can). In Danish, just like in English, modal verbs are followed by the dictionary form (infinitive) of the main verb, without using the word at before it.

Why does undersøgelsen end in -n?

This is the definite form, meaning the investigation or the study. The base noun is en undersøgelse. Because it is an en-word that already ends in an -e, you just add an -n to the end to make it definite.

Why is the adjective vigtig and not vigtigt?

Adjectives in Danish change their ending to match the noun they describe. Because undersøgelsen is a singular en-word, the adjective takes the basic form vigtig. If it were describing an et-word, it would need the -t ending to become vigtigt.