Learn Turkish: Bu teklifi kabul ettim.

The regular past tense suffix is -di, but the verb root et- ends in a hard (voiceless) consonant (t). In Turkish, when a suffix starting with d attaches to a hard consonant, it hardens to t to make it easier to say. So, et- plus -di becomes etti-. Then we add the personal suffix -m for 'I', making the final word ettim.

Where is the word for 'I' (ben) in this sentence?

You don't need it! The -m at the end of ettim is the personal subject suffix for 'I' in the past tense. Because the verb already shows exactly who did the action, it is very common in Turkish to drop the subject pronoun (ben) unless you want to strongly emphasize it.

Why does 'accepted' translate to two words (kabul ettim)?

Many Turkish verbs are made by combining a noun or adjective with a helper verb like etmek (to do/make). Here, kabul means 'acceptance' and etmek makes it an action. Together, kabul etmek means 'to accept'. When conjugating these compound verbs, only the helper verb part (etmek) gets the tense and person suffixes.

Why does the word for offer (teklif) have an -i at the end?

The -i is the specific direct object marker (often called the accusative case). Because the sentence says 'I accepted this offer' (bu teklif), we are talking about a specific, clearly defined object. Therefore, we must add the -i suffix (following vowel harmony rules) to show it is the specific target of your action.