I don't know what it is about this that you need help with....
The first letter can be any of the four given letters; for each first letter, the second letter can be any of the three remaining letters.
To make sure you get all the permutations, keep them in alphabetical order.
b --> ab
/
a - c --> ac
\
d --> ad
a --> ba
/
b - c --> bc
\
d --> bd
a --> ca
/
c - b --> cb
\
d --> cd
a --> da
/
d - b --> db
\
c --> dc