To lighten the 8 gallons of brown paint, Hamza needs to mix it with 1 gallon of white paint for every 2 gallons of brown paint.
Since the ratio is 1:2, for every 3 gallons of mixed paint (1 gallon white + 2 gallons brown), 2 gallons will be brown paint.
Therefore, for every 2 gallons of mixed paint, Hamza needs 1 gallon of white paint.
To lighten the 8 gallons of brown paint, Hamza will need half the amount of white paint compared to the amount of brown paint. So, he will need 4 gallons of white paint.
Therefore, Hamza would have to buy 4 gallons of white paint to lighten the 8 gallons of brown paint.