To find the area of the banner, we need to multiply its length by its width.
First, we need to convert the mixed numbers 2 1/3 and 6 1/4 into improper fractions:
2 1/3 = 7/3
6 1/4 = 25/4
Now, we can multiply the fractions to find the area:
(7/3) x (25/4) = 175/12
We can simplify this fraction by dividing the numerator and denominator by 1, as follows:
(175/1) ÷ (12/1) = 14.58
Therefore, the area of the banner is approximately 14.58 square feet.