There are numerous ways to achieve what you're asking for. It's a bit sad that the capx you posted didn't have any events, because it seems like you didn't even try. Always fiddle around, great things will happen. XD
Here is an example for you:
It uses a few instance variables and a global variable to create a grid movement, which once moving will only stop when it's at the position of another level tile.
Have a look at it, I hope it's helpful.