To select areas that are inside of another region/area layer, make the area layer you want to select the working layer and go to Selection>Select By Location. You can also change the selection options to adjust the behavior of this tool.
To access the selection options, open the Selection Toolbar by going to Selection>Toolbar.
Then, click on the Options button.
If you want to include features flush to the edge in your selection set, you can click on the radio button to Select Features that are Enclosed.
Then, you can go to Selection>Select by Location and choose to select features in your working layer that are inside the other area/region layer.
For a walkthrough of the selection tools, see: https://www.caliper.com/learning/media/working-with-maptitude-selection-sets-filters/