To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, 5/6 divided by 2/3 can be rewritten as (5/6) * (3/2). Multiplying the numerators gives us 15, and multiplying the denominators gives us 12. Therefore, the result is 15/12. To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 3. Dividing 15 by 3 gives us 5, and dividing 12 by 3 gives us 4. Thus, the simplified fraction is 5/4, which can be written as a mixed number as 1 1/4.