MS-Project is a scheduling and planning tool and is not well suited to time-tracking.
That said, you can set up resource calendars so that each resource is only available for 6 hours per week and Project will plan the tasks around that availability. This will give you your basic plan.
You will also need to reset Levelling to "Look for over-allocations: Weekly".
Then, if Resource A also completes Task Alpha on a particular day over and above their 6 hour allocation then simply assign that task to Resource A, set it to "Must start on" the day it was done, then mark it as complete. This will force an over-allocation against Resource A, but more importantly the "Resource Usage" view will show the total hours spent by that resource on that day. It will not calculate overtime hours for you, it will only show the total hours spent including the 6 they were meant to work- so you will have to subtract 6 hours from any day showing over-allocated to determine the overtime spent on that day.
There are potential issues with this approach in that you want to give people a pool of 6 hours per week, but Project will want to set an availability per day. So someone could exceed their daily allocation but still not exceed 6 hours per week. Without actually trying it myself I am not sure how this would pan out, you will need to experiment.
But even if you get it working I predict you will very quickly tire of doing this for such fine-grained tasks and it will become a maintenance drudge. This is because Project was not designed for time tracking. You would be better off investing in a time-tracking tool that integrates with Project, so that personnel can declare their time spent on tasks. Unfortunately I am not able to recommend such a tool, you will need to do some online research (and note that requests for toolset recommendations are off-topic for this site, but will be on-topic for the Software Recommendation SE site)