There are several ways to check your assignment submission status including looking at your Assignments tab (or whatever it might be called in your course), and the second way is to check your progress page.
1) Assignment Tab
The first way is to go to the Assignments tab, and then see if you have a green check next to the specific assignments in the list.
2) Progress Page
The second way to is to visit your "Full Progress Page" from your timeline on the home page. More details on tracking your progress here.
If you are wondering about receiving your Statement of Accomplishment, first find out which assignments are required and make sure they are marked blue, designating their completion and submission, and then check the Statement of Accomplishment requirements for your course or program.