How can I find out the number of ACTIVE Student Accounts I have within my Lt Instance?

Details of Student Accounts can be accessed from the Instance Analytics under the Instance Administration menu within Lt (you will therefore need to be an Instance Administrator to access this information).
To access this within the Instance Administration menu, go to General Settings | View Analytics:
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This will open a new tab within your Web Browser: the number of active Student Accounts is shown here:
servlet.ImageServer?id=015w0000003991p&oid=00D20000000HncM