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\frac{3\times 2y}{6y^{2}}-\frac{2}{6y^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3y and 6y^{2} is 6y^{2}. Multiply \frac{3}{3y} times \frac{2y}{2y}.
\frac{3\times 2y-2}{6y^{2}}
Since \frac{3\times 2y}{6y^{2}} and \frac{2}{6y^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{6y-2}{6y^{2}}
Do the multiplications in 3\times 2y-2.
\frac{2\left(3y-1\right)}{6y^{2}}
Factor the expressions that are not already factored in \frac{6y-2}{6y^{2}}.
\frac{3y-1}{3y^{2}}
Cancel out 2 in both numerator and denominator.