A. The teacher gave her and me the assignment.
The quickest way to figure this out is to remove the second person from this sentence:
<em>The teacher gave me the assignment. </em>
<em>The teacher gave I the assignment. </em>
Out of these two, using <u>'me'</u> is the correct option, so option A would be your only choice.
Hope this helps mate! Best of luck to you.
