Yukio is knitting a scarf that is 4 1/2 feet long, which is equal to 54 inches (since 1 foot = 12 inches). She can knit 6 inches of scarf per hour. To find out how many hours it will take her to knit the whole scarf, we divide the total length of the scarf by the length she can knit in one hour:
54 inches ÷ 6 inches/hour = 9 hours
Therefore, it will take Yukio 9 hours to knit the whole scarf.