Question 47791
The first thing that needs clarification is the term 'standard form'.
The equation happens to be in standard form already.
However, I deduce from the title, that by standard form, you want to rearrange the equation such that it is evidently a conic section. The standard form of a conic section is as follows:
{{{ ((x-a)^2)/c + ((y-b)^2)/d = r^2 }}}

This implies that you have to do some factorisation.
I assume you are familiar with completing the square.
If you are, then you will know that
{{{ x^2 - 6x = (x-3)^2 - 9 }}}
And 
{{{ y^2 - 4x = (y-2)^2 - 4 }}}
Then putting this into the original equation, we have
{{{ (x-3)^2 + (y-2)^2 = 36 = 6^2 }}}
which is in standard form.
Hooray!

When c = d = 1, we have an equation for a circle, otherwise it is an equation of an ellipse. Circles and ellipses are conic sections.