You can do an Aggregate Query for each of your tables to pull the latest date for each person, i.e.
Code:
SELECT PatientID, Max(EnrollDate)
FROM EnrollTable
GROUP BY PatientID
and
Code:
SELECT PatientID, Max(DischargeDate)
FROM DischargeTable
GROUP BY PatientID
You can then join those two queries together in another query, joining on the PatientID field, and return the latest Enrollment and Discharge dates and compare them.
Note, I would probably recommend doing a LEFT OUTER JOIN from the Enroll Query to the Discharge Query, because it may be possible that someone has one enrollment and zero discharges (they haven't been discharged yet).
That way you won't lose any records. You can use the Nz function on the MaxDischargeDate field to handle those nulls.