Your role in the accident must be less than 51% in order to request damages from the other driver. The amount you get, however, is reduced by the percent your action (or inaction) played in the crash.
The adjuster from the other driver's insurance company has a detailed claim file that may include statements from drivers and third parties, damage inspections, a crash report and more. Based on the investigation in this case, the adjuster determined you were 20% responsible for the crash. Perhaps you were driving too fast for conditions, did not use a turn signal, failed to yield at an intersection or contributed to the accident in some other way.
Talk to the insurance adjuster if you disagree with the claim offer. Or, turn the loss into your company if you have collision coverage.. Ultimately only a court can determine the amount of damages owed.