First, find the unit rate.
Since the car travels 476 miles with 14 gallons of gas, then 476/14 = 34, so the car can travel 34 miles per gallon.
The distance is 34 times the number of gallons
d = 34g
Now you are given 578 miles, and you need to find the gallons.
578 = 34g
Solve for g by dividing both sides by 34.
g = 17
He needs 17 gallons.