i am assuming that the area of both the sides are equal  assuming

charge on outer side of the x to be q1   and on the inner side of q-q1

charge on the inner side of  y  is -(q-q1)    because if we draw a gaussian surface passing thru the conductore the electric field inside should be -(coz of conduction properties)

charge on outer side=q-q1

the electric field at any pnt x or y =0 as it is inside the conductor

so        

so  q-q1=q  solving we get   q1=q2

so now we can get the all the answers easily