Firstly, we will draw figure
Let's assume
length of AC=x
we have
AB : BC = 2 : 1
so,


Point D is on line AB
and

AD : DB = 3 : 2
so, we get




now, we can locate these values
Firstly, we will find DC
DC=DB+BC
now, we can plug values


we have got

now, we can find ratio

now, we can simplify it

so,
AD:DC=2:3...........Answer