To solve this expression, we need to find a common denominator for the fractions. The common denominator for 4, 8, and 3 is 24.

Now, let's convert each fraction to have a denominator of 24:

7/4 = (7/4) * (6/6) = 42/24
5/8 = (5/8) * (3/3) = 15/24
2/3 = (2/3) * (8/8) = 16/24

Now, we can rewrite the expression with the common denominator:

42/24 - 15/24 + 16/24

To combine the fractions, we can simply add or subtract the numerators while keeping the denominator the same:

(42 - 15 + 16)/24 = 43/24

Therefore, the simplified expression is 43/24.