Answer:
H=Hyperbola
L=line
C=circle
P=Parabola
First letter is top one:
HL=0, 1, 2
LP=0, 1, 2
LC=0, 1, 2
LH=0, 1, 2
PP=0, 1, 2, INFINTELY MANY
PC=0, 1, 2,
PH=0, 1, 2, 3
CP=0, 1, 2
CC= 0, 1, 2, INFINITELY MANY
CH=0, 1, 2, 3, 4
HP=0, 1, 2, 3
HC=0, 1, 2, 3, 4
HH=0, 1, 2, 3, 4, infinitely many