Answer
12 possible outcomes
Work Step by Step
$\ \ \ \ \ $$\ \ \ \ \ $$\ \ \nearrow$ 1
$\ \ \ \ \ $$\ \ \ \ \ $M$\rightarrow$ 2
$\ \ \ \ \ $$\ \ \ \ \ $$\ \ \searrow$ 3
$\ \ \ \ \ $$\ \ \ \ \ $$\ \ \nearrow$ 1
$\ \ \ \ \ $$\ \ \ \ \ \ $A$\rightarrow$ 2
$\ \ \ \ \ $$\ \ \ \ \ $$\ \ \searrow$ 3
$\nearrow$
$\nearrow$
$\searrow$
$\searrow$
$\ \ \ \ \ $$\ \ \ \ \ $$\ \ \nearrow$ 1
$\ \ \ \ \ $$\ \ \ \ \ \ $T$\rightarrow$ 2
$\ \ \ \ \ $$\ \ \ \ \ $$\ \ \searrow$ 3
$\ \ \ \ \ $$\ \ \ \ \ $$\ \ \nearrow$ 1
$\ \ \ \ \ $$\ \ \ \ \ \ $H$\rightarrow$ 2
$\ \ \ \ \ $$\ \ \ \ \ $$\ \ \searrow$ 3