What can I do if my employer asked me to haul some bookshelves in the back of my truck but once I got back to work 1 of the shelves fell into my truck and put a hole in the tailgate?

They are not necessarily legally required to pay for the repairs the fact that you were using your truck for work or hauling your employer's property does not automatically make the employer responsible to pay for the repairs, any more than if you had volunteered to help a friend move and you dropped a bookshelf on your truck, holing it, your friend would have to pay. Rather, the obligation to pay, or fault, depends on liability if your employer was somehow "at fault" in causing the damage, then they might be liable. For example, if a co-worker tripped and knocked over the shelf, causing damage, the employer could be liable due to your co-worker's fault. But if only you were at fault e.g. you didn't secure the shelves correctly, or if no person was at fault, then the employer is not at fault if the accident occured without any fault, no one is responsible for it, and if you were at fault, even though you are an employee, you cannot receive compensation for you own careless act. So the issue is why did the shelf fall this way, and was it the employer's fault or the fault of a co-worker--if it was, you could seek compensation. Of course, even if your employer were liable, if they won't pay voluntarily, you'd have to sue for the money, and suing your employer can have its own significant negative consequences.