Learn Finnish: Toimittaja tiedusteli asiaa rehtorilta. - The journalist inquired about the matter from the principal.

This is the core rule for verbs of asking! With verbs like tiedustella (to inquire) and kysyä (to ask), the person you are asking is put into the ablative case (-lta/-ltä). In Finnish, you literally ask for information 'from' or 'off of' someone.

Why is the object asiaa in the partitive case rather than the accusative?

The verb tiedustella almost always takes a partitive object. When you inquire about a matter (asia), it is treated as an open-ended or abstract action rather than something you physically complete or consume, so it requires the partitive ending -a.

How did the verb tiedustella turn into tiedusteli?

The base verb is tiedustella, which is a Type 3 verb. To form the past tense (imperfekti), you drop the final -la to get the stem tiedustel-, and then add the past tense marker -i. Because this is the 3rd person singular (he/she) form, no extra personal ending is added, leaving us with tiedusteli.

Could I just use 'kysyi' instead of 'tiedusteli' in this sentence?

Yes, you absolutely could say 'Toimittaja kysyi asiaa rehtorilta'. Both verbs use the exact same sentence structure, including the -lta ending for the person being asked. The difference is just the tone: tiedustella is a bit more formal, like 'inquire', while kysyä is the everyday word for 'ask'.