Explanation:
what is the question ?
how much water does the full bucket contain ?
if so, then I understand that
11 2/3 gallons = 5/6 bucket
(11×3 + 2)/3 gallons = 5/6 bucket
35/3 gallons = 5/6 bucket
what do we need to do to get 1 bucket (5/5 or 6/6 or 3/3 or ...) on the right side ?
we multiply everything by 6/5 :
35/3 × 6/5 gallons = 5/6 × 6/5 bucket
(6×35)/(5×3) gallons = 1 bucket
(2×7)/(1×1) gallons = 1 bucket
14 gallons = 1 bucket
the bucket can contain 14 gallons of water.