How many tomatoes does it take for a gallon of sauce? Once you know that multiply that number by 3 if that number is bigger than (6*25=)150 then no 6 vines will not be enough.
You will have to make some assumptions about the size of the tomatoes and the amount of sauce you can get from each.
Assume each tomato is 3 inches in diameter. The volume of one tomato is 4/3 X pi X 1.5^3 or about 14.1 cubic inches.
6 X 25 X 14.1 = 2115 cubic inches of tomatoes. One gallon contains 231 cubic inches so 3 gallons will contain 693 cubic inches. 6 vines should be plenty.
If on the other hand the tomatoes are 2 inches in diameter you will get 4/3 X pi X 16^3 X 6 X 25 = 628 cubic inches of tomatoes.
This would not be enough.
tomatoes don't grow on vines... nice try though!
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