Convert \( 6 \frac{1}{6} \) and \( 3 \frac{5}{6} \) to improper fractions: \[ 6 \frac{1}{6} = \frac{6 \times 6 + 1}{6} = \frac{37}{6} \] \[ 3 \frac{5}{6} = \frac{3 \times 6 + 5}{6} = \frac{23}{6} \]
Subtract the two fractions: \[ \frac{37}{6} - \frac{23}{6} = \frac{37 - 23}{6} = \frac{14}{6} \]
Simplify \( \frac{14}{6} \) by dividing the numerator and denominator by 2: \[ \frac{14}{6} = \frac{7}{3} \]
\(\boxed{\frac{7}{3}}\)
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