The given expression is a subtraction of mixed numbers. To subtract mixed numbers, we first convert them into improper fractions. Then, we find a common denominator and subtract the fractions. Finally, we convert the result back into a mixed number if necessary. In this case, 4 1/6 is equivalent to 25/6 and 3 3/8 is equivalent to 27/8. The common denominator is 24. Subtracting the fractions, we get (25/6) - (27/8) = (100/24) - (81/24) = 19/24. Therefore, the answer is 19/24.