Collocations for assignment - noun

special
important
dangerous, difficult, tough
job (esp. AmE), work
modelling/modeling, photographic

accept, take on
Why did you take on this assignment if you're so busy?

get, have, receive
carry out
refuse
If you refuse this assignment you risk losing your job.

complete, finish
give sb

on assignment
The photographer is on assignment in China at the moment.

reading, writing, written
homework
class, group (both esp. AmE)

give, hand out, set (esp. BrE)
The teacher gave us an assignment on pollution.

get, receive (esp. AmE)
do, write (esp. AmE)
read
complete, finish
hand in
The students handed in their assignments.

assignment on
an assignment on modern lifestyles