If you are talking in terms of Using FileMaker clients to access a hosted database (hosted by FileMaker Server or FileMaker Pro), then this can be done. The more layouts you have, the more time this will take to set up as you'll need layout script triggers on every layout that log this information into a table defined for the purpose.
Use manage | security to assign account names and passwords.
OnLayoutEnter and OnLayoutExit are script triggers you can put on every layout. (may not need to use both) That run a common script that captures the name of the layout, the account name and/or user name and the current time stamp, logging all this data into a table where you have a field defined for each such item. Calculation fields can then compute the elapsed time.
To log initial access and final exit, you can use FileOptions to specify that a script be run when the file is opened and also when it is closed, but if you log each time a layout is entered and exited, you will not need these as the first layout entered will be the date and time they signed on and the last layout exited would be the time they exit the program.
Please note that if the client copy of filemaker crashes or communication with the host is interrupted (can be done as easily as unplugging the ethernet cable to the workstation), the last "exit" event cannot be captured.
A summary report based on this access log table can be designed to summarize the time spent accessing the database with subtotals for time spent on each layout.