There's a decimal missing somewhere, so I'll just add it wherever, and if it's not correct it shouldn't be to difficult to figure out what to do to fix it.
[tex]x=0.6\overline{72}=0.6727272\ldots[/tex]
[tex]10x=6.\overline{72}=6.727272\ldots[/tex]
[tex]1000x=672.\overline{72}=672.727272\ldots[/tex]
[tex]\implies1000x-10x=990x=666\implies x=\dfrac{666}{990}=\dfrac{37}{55}[/tex]
