How to use the past perfect correct?

Hello~ I am a ESL learner from Taiwan.
I have a question about the past perfect.
The question is as follows:

I finished the assignment my boss gave me, or had given me before schedule.

Which one is correct? If you know the reason behind it, please kindly tell me more about it.

once I raised the question to a Professor of English, a kind and nice native speaker, but it seems that her explanation still dose not give me assurance that I can decide in which condition I should the use of past tense or the past perfect in sentences.