To subtract these fractions, we need to find a common denominator first. The least common multiple of 6 and 14 is 42.

Rewriting the fractions with the common denominator of 42, we get:

[tex] \frac{35}{42} - \frac{27}{42} [/tex]

Now we can subtract the numerators to get:

[tex] \frac{35 - 27}{42} = \frac{8}{42} [/tex]

Simplifying the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2, we get:

[tex] \frac{4}{21} [/tex]

So, [tex] \frac{5}{6} - \frac{9}{14} = \frac{4}{21} [/tex]