$\frac{ 2\left( y-2 \right) }{ 4y } \times \frac{ 9{y}^{2} }{ 27y-54 }$
Factor out $27$ from the expression$\frac{ 2\left( y-2 \right) }{ 4y } \times \frac{ 9{y}^{2} }{ 27\left( y-2 \right) }$
Cancel out the common factor $y$$\frac{ 2\left( y-2 \right) }{ 4 } \times \frac{ 9y }{ 27\left( y-2 \right) }$
Cancel out the common factor $y-2$$\frac{ 2 \times 1 }{ 4 } \times \frac{ 9y }{ 27 }$
Cancel out the common factor $2$$\frac{ 1 }{ 2 } \times \frac{ 9y }{ 27 }$
Cancel out the common factor $9$$\frac{ 1 }{ 2 } \times \frac{ y }{ 3 }$
Multiply the fractions$\frac{ y }{ 6 }$