The value of a Damascus hammerless double barrel shotgun with serial number 35632 can vary significantly based on factors such as its condition, provenance, and market demand. Generally, these shotguns can range from a few hundred to several thousand dollars. For an accurate appraisal, it's best to consult a firearms expert or appraiser who can evaluate the specific piece in person. Additionally, checking recent sales of similar models can provide insight into current market values.