Why does the momentum of a billiard ball rolling on a billiard table change?

If the billiard ball is going at the constant speed and contains its mass then the momentum WONT be changing. But realistically you have external forces like friction and air resistance changing the velocity thus changing the momentum. In this case momentum is not conserved because you're introduction an external force.

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s