To find x, we can set up a proportion:

2/8 = x/14 2/3

First, convert the mixed number 14 2/3 to an improper fraction:

14 2/3 = (3*14 + 2) / 3 = 44/3

Now plug in the values into the proportion:

2/8 = x / 44/3

Simplify the left side of the equation:

2/8 = 1/4

Now solve for x:

1/4 = x / 44/3
1/4 = x / (44/3)
1/4 = x * 3/44
1/4 = 3x / 44
44 = 12x
x = 44 / 12
x = 11/3 or approximately 3.67

Therefore, x is approximately 3.67.