Let  $a=3\sqrt{2}$  and  $b=\frac{1}{5^{\frac{1}{6}}\sqrt{6}}$. If  $x,y\in R$  are such that 
$3x+2y={\log }_a{\left(18\right)}^{\frac{5}{4}}$  and 
 $2x-y={\log }_b\left(\sqrt{1080}\right)$ , 
Then  $4x+5y$  is equal to________.

 $a=3\sqrt{2}\Rightarrow a^2=18$
Notice that  $1080={5.6}^3\Rightarrow$
 $5^{\frac{1}{6}}{.6}^{\frac{1}{2}}={\left(1080\right)}^{\frac{1}{6}}=\frac{1}{b}\Rightarrow {1080}^{\frac{1}{2}}=\frac{1}{b^3}$
 $\Rightarrow 3x+2y={\log }_a{\left(a^2\right)}^{\frac{5}{4}}=\frac{5}{2}$  ………… (i)
 $2x-y={\log }_b\frac{1}{b^3}={\log }_b{b}^{-3}=-3$  ………… (ii)
$\Rightarrow$ solving (i) &(ii)
 $\Rightarrow x=\frac{-1}{2},y=2\Rightarrow 4x+5y=8$