Answer
$(a)$ Symmetry with respect to $x$-axis
$(b)$ $x$-intercept $B(6,0)$
$y$-intercepts $A(0,6)$ and $C(0,-6)$
Work Step by Step
$(a)$ As we can see from the image of the graph above, it is symmetrical with respect to the $x$-axis.
Algebraically, if we replace $y$ by $-y$ equation will be still equivalent to the original one.
$(b)$
$x$-intercept happens when $y=0$
$6x+0^2=36$
$6x=36$
$x=6$
$B(6,0)$
$y$-intercept happens when $x=0$
$6\times0+y^2=36$
$y^2=36$
$y=±6$
$A(0,6)$ and $C(0,-6)$