So essentially, we have a choice of :
2 reception halls
3 DJs
2 catering companies.
In order to find the number of arrangements, you need to multiply those : 2*3*2=12- So they have 12 arrangements.
why?
Imagine those 3 Djs- they are three arrangements.
Now, they can play in one or the other hall -so in total it's 3 Djs in one hall and 3 in the other -that's 6.
And all of those 6 possibilities can be catered by one or the other company- making the possibilities twice as many, so it's 12 in total!