Questions & Answers about Я хочу поблагодарить учителя за совет.
Yes. Хотеть (to want) is normally followed by an infinitive: я хочу сделать, она хочет поехать, etc.
So Я хочу поблагодарить… = I want to thank… (literally: I want to thank).
This is about aspect:
- благодарить (imperfective) = to thank (as a process/habit, or generally)
- поблагодарить (perfective) = to thank once, as a completed action
With Я хочу…, Russian often uses perfective to mean “I want to do it (and complete it)”: Я хочу поблагодарить = “I want to thank (and get it done).”
Because учитель is an animate masculine noun, and in the accusative case singular it usually looks like the genitive:
- Nominative: учитель (the teacher)
- Accusative (whom?): учителя (the teacher, as the direct object)
So поблагодарить (кого?) учителя.