Learn Turkish: Otel odasını ben halledeyim mi? - Shall I sort out the hotel room?

The base verb is halletmek (to sort out, handle). To make it an offer (let me / shall I), we use the optative suffix -e followed by the 1st person singular suffix -yim. So halled- + -e + -yim gives us halledeyim. The separate question particle mi at the end turns the offer into a question: Shall I sort it out?

Why does halledeyim have a d if the verb is halletmek?

This is consonant mutation. When verbs ending in -tmek or -tmak (like halletmek, gitmek, or etmek) are followed by a suffix starting with a vowel (like the optative -e), the t softens to a d. So hallet- becomes halled-.

What suffixes are attached to odasını?

The base word is oda (room). First, we add the possessive suffix -sı to link it to otel, making the compound noun otel odası (hotel room). Because this specific room is the direct object of the action, we must add the accusative suffix -ı. The n in the middle is a buffer letter to keep the two vowels apart, giving us oda-sı-n-ı.

Why include the word when the verb already means I will / shall I?