"Final exam" 和 "final assignment" 都是指期末作业。
"Final exam" 是 "final examination" 的缩写，是指学期末考试。
"Final assignment" 是指学期末作业。
例句：
I have a lot of final exams next week. 我下周有很多期末考试。
I need to finish my final assignment before the deadpne. 我需要在截止日期前完成我的期末作业。
The final exam for the course is next Friday. 这门课的期末考试是下周五。
I've been working on my final assignment all week. 我整个星期都在做我的期末作业。