complete the square for both x and y ...
$\displaystyle 6x^2 - 12x + 7y^2 + 42y = 57$
$\displaystyle 6(x^2 - 2x) + 7(y^2 + 6y) = 57$
$\displaystyle 6(x^2 - 2x + 1) + 7(y^2 + 6y+9) = 57 + 6 + 63$
$\displaystyle 6(x-1)^2 + 7(y+3)^2 = 126$
$\displaystyle \frac{(x-1)^2}{21} + \frac{(y+3)^2}{18} = 1$
you should recognize the above general form equation for an ellipse.
if you wish to graph it in your calculator, you'll have to solve for y, getting equations for the upper and lower branches of the ellipse and graphing those in Y1 and Y2.