First we need to find the area of the fence, since paint covers square feet and squared units refers to area. The area of the fence is 26 x 7, which is 182 sq ft. If one gallon of paint will cover 350 sq ft, your proportion will look like this, with gallons of paint on top and square feet on the bottom. 
. Cross multiply to get 350x = 182 and x = .52, just a bit over a half of a gallon of paint.