The button that allows you to see the path you draw on a solid is the one associated with toggling mask and shape path visibility. This functionality is crucial for working with shapes and masks in After Effects, as it provides a clear view of the paths you create directly on your layers. When this option is enabled, you can see the outlines and parameters of your shapes and masks, which helps in precisely editing and adjusting your designs visually.
This feature is particularly beneficial during the animation process, as it allows you to track and manipulate paths easily. Being able to visualize the paths you are working on enhances workflow efficiency, especially when you're dealing with intricate designs or layering multiple shapes.
The other options pertain to different aspects of layer management in After Effects. However, they do not directly relate to showing the paths drawn on solids, making them less relevant to the task at hand.