bearing in mind that, parallel lines have the same slope, hmmm what's the slope of 9x - 3y = 27 anyway?
[tex]\bf 9x-3y=27\implies -3y=-9x+27\implies y=\cfrac{-9x+27}{-3} \\\\\\ y=\cfrac{-9x}{-3}+\cfrac{27}{-3}\implies y=\stackrel{\stackrel{m}{\downarrow }}{3}x-9\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
well, a parallel line to that one will also have the same slope, namely, we're really looking for the equation of al line whose slope is 3 and runs through (6,2).
[tex]\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{2})~\hspace{10em} \stackrel{slope}{m}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{3}(x-\stackrel{x_1}{6}) \\\\\\ y-2=3x-18\implies y=3x-16[/tex]
