In this situation, Peter's insurance company will pay for the damages to the car, minus the deductible. The deductible is the amount of money that the insured party (in this case, Peter) is responsible for paying before the insurance company will cover the rest of the damages.
Since Peter has a $1000 deductible and the damages to the car are $4300, the insurance company will pay $4300 - $1000 = $3300 for the damages.
So, in this case, the insurance company will have to pay $3300 to cover the damages to Peter's car.