Learn Turkish: Suçu işlediğini inkâr etti. - He denied that he committed the crime.

This uses the -dIk factive clause structure you are currently learning. It breaks down like this: işle (commit) + -diğ (the past/present suffix -dik, softened due to the vowel) + -i (his/her, the possessive suffix) + -n- (buffer letter) + -i (accusative case). Literally, it translates to "his having committed", and the accusative case marks the whole chunk as the direct object of the main verb inkâr etti (he denied).

Why do both suçu and işlediğini take the accusative case?

They are objects for two different verbs! Suçu (the crime) is the direct object of the inner verb işlemek (to commit). Then, the entire clause suçu işlediğini (that he committed the crime) becomes the direct object of the main verb, inkâr etti (he denied). Because of this, işlediğini gets its own accusative ending.

Could işlediğini also mean "that you committed"?

Yes, it absolutely could! Out of context, işlediğini is ambiguous. It could be işlediği (his/her committing) + -n- (buffer) + -i (accusative), OR it could be işlediğin (your committing) + -i (accusative). Without pronouns like onun (his) or senin (your) at the start of the sentence, we rely on context. Here, "He denied that he committed the crime" is the most logical translation.