Am I liable for a mailbox damage if it extends into the road 6"?

You are liable for the damage to the mailbox which would include the cost of repairs or replacement with a new mailbox.

You can refer the matter to your auto insurance company and the company will handle it for you.  If it is not much of an expense, you might want to consider just paying for it without dealing with the insurance company and a possible future rate increase.

If the case is not resolved by the owner of the mailbox with you or your insurance company, the owner could file a lawsuit in Small Claims Court against you for negligence.  The owner's damages (the amount of compensation the owner is seeking to recover in the lawsuit) would be the cost of repair or replacement of the mailbox.  The owner has to mitigate (minimize) damages by having the mailbox repaired or replaced at reasonable cost.  If the owner selected the most expensive place for repairs or purchased an expensive mailbox not comparable to the damaged one, the owner would have failed to mitigate damages and the owner's damages would be reduced accordingly.