A living hinge uses the same material as the container or board to bend. This can be down with plastic by making the hinge thinner than the surrounding plastic. In less pliable materials like wood, a living hing can be made by removing material in a pattern than makes the material more flexible. There are many different patterns  to use with living hinges. A simple alternating brick pattern of incisions is a straightforward and predictable way to make living hinges with a laser cutter.

In Fusion 360 , living hinges can be made with a sketch directly without testing the bend. If a narrow spacing for the cuts is used the living hinge will likely bend fine. For more accurate living hinges, you can use the sheet metal tools in Fusion 360 to define a specific thickness and bend radius.

You can get the bend radius of a material you are making by first cutting living hinge test swatches  with the laser cutter and measuring the bend with a radius gauge. Then you can design to the bend limit of the particular material you are working with.

If you want to work with living hinges in your laser cut project, it is a good idea to ask for assistance from your instructor.