Final answer:
The element that means 'after' is 'post.' It is a prefix deriving from Latin to indicate the occurrence of events after a specific time.
Step-by-step explanation:
The correct element that means "after" is post. This prefix is derived from Latin and is commonly used in English to indicate that something happens after a certain event or time. For example, postgraduate refers to studies undertaken after graduating with a first degree, and postwar refers to the period after a war has ended.
The other options provided do not mean "after": 'em' is not commonly used as a prefix with a specific meaning, 'mort' relates to death (such as in mortality), 'auto' means self (as in automobile or automatic), and 'patho' refers to disease or suffering (as in pathology).