[tex]\displaystyle \\
\frac{2}{3} :\left(\frac{1}{4}+\frac{1}{2}\right)\times \frac{27}{4}= \\ \\
=\frac{2}{3} :\left(\frac{1}{4}+\frac{2}{4}\right)\times \frac{27}{4}= \\ \\
=\frac{2}{3} :\left(\frac{1+2}{4}\right)\times \frac{27}{4}= \\ \\
=\frac{2}{3} :\frac{3}{4}\times \frac{27}{4}=\frac{2}{3} \times\frac{4}{3}\times \frac{27}{4}=\frac{8}{9} \times \frac{27}{4}= 2\times 3 =\boxed{6} [/tex]
