)with the box still on the truck, the truck attains its maximum velocity. as the truck comes to a stop at the next stop light, what is the magnitude of the maximum deceleration the truck can have without the box sliding?

When the truck starts decelerating a force starts acting on a box. In order for the box to start sliding force acting on it has to be bigger than a static force of friction. 
If the trucks declaration is we have the following force acting on the box:

This force has to be smaller than static friction force:

Where is static friction coefficient.
Now we can find an

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Where is the table ? you can take a picture of it