Figure out means to understand something after thinking about it. Find out means to get information, often from another person, a message or research. If you solve the logic of how something works, figure out is usually better.

Fall apart can describe a physical object breaking, but it can also describe a plan, relationship, organisation or person losing stability. Here it means the plan failed because an important part disappeared.

Face up to means to accept that a difficult or unpleasant situation is real and start dealing with it. It is stronger than just face because it often includes honesty and responsibility.

Come up against means to face or meet a problem, difficulty or opposition. It is more specific than simply meet because it suggests that something makes progress harder.

Back up has several meanings. It can mean support someone, make a backup copy of data, or move backwards. In a meeting, back you up means support your opinion or help you defend your position.

Count on means rely on. It needs an object: count on me, count on your team, count on good weather. You cannot normally use it without saying who or what you rely on.

Cover up can literally mean to cover something physically, but at B2 level it is often used to mean hide the truth about a mistake, crime, scandal or embarrassing situation.

Set up can mean start a company, organise a meeting, prepare equipment or configure a system. In this sentence, set up a business means start or establish it.

Turn down has two common meanings: refuse an offer, invitation or request; or reduce the volume, heat or light. In this sentence, turn down the job offer means refuse it.

Bring about means to cause something to happen, especially a change, result or consequence. It is often used in more formal contexts, such as politics, business, social changes or long-term results.