Learn Turkish: Bugün projeyi bitirmedik. - We didn't finish the project today.

The -yi is the specific direct object suffix (often called the accusative case). Because we are talking about a specific project (the project, rather than just a project), we have to add this ending to the thing being finished. The y is simply a buffer letter used because proje ends in a vowel.

How do you build the verb bitirmedik?

It starts with the verb root bitir (finish). Then we add the negative suffix -me, followed by the past tense suffix -di. Finally, we add -k, which is the personal ending for we in the past tense. Put together, bitir-me-di-k literally builds finish-not-past-we.

Why is the negative suffix -me here instead of -ma?

This happens because of vowel harmony. Suffixes change their vowels to match the word they attach to. The last vowel in the verb root bitir is i, which is a front vowel. Therefore, the negative suffix must use the front vowel e to become -me rather than the back vowel a (-ma).

Could I put biz (we) at the beginning of the sentence?

Yes, you could say Biz bugün projeyi bitirmedik. However, because the -k at the very end of bitirmedik already tells us exactly who didn't finish the project, dropping biz is completely natural and the most common way to speak in Turkish.