How to mount a PCB in a project box
I like to choose project boxes that have a smoother inside bottom surface than the one you show in your picture. Those specialized mount points can get in the way of trying to use the standoffs that you show. 

With that said the best strategy is to get a box that has molded in standoffs. Then you specially design your PCB to have mounting holes that match these standoffs.

However if you are making a prototype or one-off hobby project then I can suggest doing as I have. I drill holes through the bottom of the box in the correct locations to mount the type of standoffs as you show. These holes are then countersunk with and a flat head machine screw inserted from the outside is used to secure the nylon standoff on the inside. If you do not plan to remove these screws for disassembly the it is possible to back fill the screw head counter sink with epoxy  provided the screw head is below the outside surface on the bottom side.