He is not bad at badminton.
When believe means accept as true it is used without a preposition.
I won’t believe a word you say.
Do you believe in ghosts?
Belong in / on (= have its place in / on)
Those books belong on the top shelf.
Belong to (= be a member of)
I belong to a local athletics club.
Blue with, red with, green with etc.
She went green with envy.
She is not very clever at singing.
Congratulate somebody on something
I must congratulate you on your success.
Congratulate on / for doing something
He congratulated me on / for having won the first prize.
The car crashed into a tree.
Depend on / dependent on
We might cancel the trip – it depends on the weather.
He is dependent on his parents.
Write now for details of our special offer.
Die of / from
He died of Malaria.
A week after the accident he died from his injuries.
Difficulty with something / difficulty in doing something
I have difficulty with my travel arrangements.
We had no difficulty in finding his address.
Disappointed with somebody
He is disappointed with his son.
Disappointed with / at / about something
I am disappointed with my performance.
We had a long discussion about philosophy.
Note that the verb discuss is used without a preposition.
Let’s discuss your plans. (NOT Let’s discuss about your plans.