User wants to set a constraint to an activity so that the project will not go over a specific date.

The finish constraints can be set at the activity level in the status tab. In the past I have suggested Finish On as the type for an activity that needs a hard finish date. The finish on constraint can delay an early finish or accelerate a late finish to satisfy the imposed date. There is also a project level constraint that can be used called the Must Finish By date. It’s a date constraint placed on the project end date. When you edit the must finish by date, the calendar defaults to the date and time currently in the Must Finish By field. This constraint will be the starting point for the Backward Pass (i.e. the calculation of the Late dates) when the Project is Scheduled. Project Must Finish by Constraints only affects the late dates of a Project.