help with index and match that returns value based on multiple criteria

Hello,

Thanks GeoffW283 for your response! I tried the formula but it doesnt produce the desired results. For example I entered it in cell B5 of the "TASK_COMPLETION_LIST" tab and it gives back a date which does not correspond to the date that subject completed the task. The date each subject completed each task is in the "CALENDAR" tab.I attached another excel file which I think is clearer. The desired results are in rows 2 and 3 of the "TASK_COMPLETION_LIST" tab.