no of orange U can get is given by $(x^{4}+x^{5}+x^{6}+x^{7}+x^{8})$
no of orange V can get is given by $(x^{2}+x^{3}+x^{4}+x^{5})$
no of orange W can get is given by $(x^{2}+x^{3}+x^{4}+x^{5}+x^{6})$
Hence finding the coefficient of $x^{12} $ in the equation
$(x^{4}+x^{5}+x^{6}+x^{7}+x^{8})$ * $(x^{2}+x^{3}+x^{4}+x^{5})$ * $(x^{2}+x^{3}+x^{4}+x^{5}+x^{6})$ = $x^{12} $
$x^{4} $( $ \frac{1- x^{5} }{1-x}$) * $x^{2} $( $ \frac{1- x^{4} }{1-x}$) * $x^{2} $( $ \frac{1- x^{5} }{1-x}$) = $x^{8} $ $( 1- x^{5} )*( 1- x^{4} ) *( 1- x^{5} )*({1-x})^{-3}$
Coffiecient of $x^{4 } $ in $( 1- x^{5} )*( 1- x^{4} ) *( 1- x^{5} )*({1-x})^{-3}$ is
$_{6}^{4}\textrm{C}$ - $_{2}^{0}\textrm{C}$ = 15 -1 =14