lily has 13 yards of clothes
the total clothes length used by lily is
[tex]=2\frac{6}{4}+3\frac{1}{3}+4.5[/tex][tex]\begin{gathered} =\frac{14}{4}+\frac{10}{3}+\frac{45}{10} \\ =\frac{14}{4}+\frac{10}{3}+\frac{9}{2} \end{gathered}[/tex]so remaining yards is
[tex]=13-(\frac{14}{4}+\frac{10}{3}+\frac{9}{2})[/tex][tex]\begin{gathered} =13-(\frac{42+40+54}{12}) \\ =13-\frac{136}{12} \end{gathered}[/tex][tex]=\frac{156-136}{12}=\frac{20}{12}=\frac{5}{3}[/tex]