To simplify the expression, we need to simplify each term separately and then combine them.

Let's start with the first term: 7/3√27.

√27 can be simplified as √(9*3) = √9 * √3 = 3√3.

So, the first term becomes 7/3 * 3√3 = 7√3.

Now let's simplify the second term: 4√12.

√12 can be simplified as √(4*3) = √4 * √3 = 2√3.

So, the second term becomes 4 * 2√3 = 8√3.

Finally, let's simplify the third term: 1/3√192.

√192 can be simplified as √(64*3) = √64 * √3 = 8√3.

So, the third term becomes 1/3 * 8√3 = 8/3√3.

Now we can combine the simplified terms:

7√3 - 8√3 + 8/3√3

Since all the terms have the same radical, we can combine them by adding or subtracting the coefficients:

(7 - 8 + 8/3)√3

Simplifying the coefficients:

(7 - 8 + 8/3)√3 = (-1 + 8/3)√3 = (-3/3 + 8/3)√3 = (5/3)√3

So, the simplified expression is (5/3)√3.