Your monthly usage period begin and end dates depend on when you signed up for your Cloud account.
To see the begin and end date of your current period, go to your Account Overview page. To get there, click on your name on the right side of the header, then click on Account. If needed, you can see the Individual Account section of the Guide (https://rstudio.cloud/learn/guide#accounts) for more details.
This also might be of interest to you - we released a new low cost plan yesterday, called the Plus plan. If you are happy with the Free plan features, but just need additional hours, this plan might make sense for you. More details are at https://rstudio.cloud/plans/plus.
We are also working on two additional features which we hope to release in the next few weeks - one will let you download projects without opening them, so even if you've used up your monthly allotment of hours on the Free plan, you'll be able to export your projects and work on them locally. The second is that we will give you a "grace period" when you reach your hours limit - we'll send you an email letting you know you've reached your limit for the month, but you'll be able to continue to access your projects for the next 48 hours.
Hope this helps - and please let us know if you have additional questions.