Mary, James, and Carlos sold \(\dfrac{1}{4}\)-page advertisements for the school yearbook. Mary sold twice as many as Carlos did, and James sold 3 times as many as Mary did. What fraction of these advertisements did Carlos sell?

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Mary sold twice the amount as Carlos:

$$ M = 2C $$

James sold three times as much as Mary:

$$ J = 3M $$ $$ J = 3(2C) $$ $$ J = 6C $$

The total:

$$ C + M + J $$ $$ C + 2C + 6C $$ $$ = 9C $$

Therefore, Carlos sold:

$$ \frac{C}{9C} = \boxed{\frac{1}{9}} $$