Answer
4
Work Step by Step
We first combine this into one square root:
$1/3 \sqrt {6\times 24} = 1/3 \sqrt {144}$
We see if any of the factors of a radical are perfect squares (meaning that their square root will be an integer) to see if the radical is in its most simplified form. We see that 144 is a perfect square, so we know that we can simplify:
$1/3 \sqrt {144}=12/3=4$