Checkboxes are a good way of asking multiple choice questions with more than one correct answer. Here's how they're put together in Open edX.
From edX Studio, navigate to the unit of your course where you would like to add a problem, then select the "Problem" button.
You'll now be presented with a list of different problem types. Select "Checkboxes."
You should now see something that looks like the image below. In order to edit your question. Click "Edit" on the upper right.
This is the Simple Editor where you edit simply. In order to change anything, all you have to do is type, but be mindful of how edX has the problems formatted, and try remain within those boundaries.
When you finish editing your question, be sure to hit Save!
That's all there is to it!