A 12 year old dog is after all approximately equivalent to a 70 year old human so it is not abnormal for a dog of his age to find exercise difficult, and a slowing down of the cardiac or pulmonary system is usually responsible for such symptoms.

This means that either the heart is not pumping fast enough or efficiently enough to supply the lungs with sufficient oxygen, or the lungs are not exchanging the oxygen for the carbon dioxide quickly enough, hence the shortness of breath. Your vet will be able to carry out various tests to indicate what the exact problem is and in some cases can prescribe drugs to help ease the symptoms. A change in exercise routine to include more rests and a shorter walk would certainly be something to think about.