work something out   
phrasal verb with work verb uk/wɜːk/ us/wɝːk/
  (CALCULATE)      
 B2 计算出
to do a calculation to get an answer to a mathematical question
  We need to work out the total cost of the project. 我们需要算出这项工程的总造价。 
 - More examples
 - Can you work out how much each card cost?
 - I need to work out how much tax I will have to pay.
 - When we worked out how much it cost us to run a car, we decided to sell it.
 
  (UNDERSTAND)      
C2 (US usually figure sth out)理解;想出 
to understand something or to find the answer to something by thinking about it
  [ + question word ] There will be a full investigation to work out what caused the accident. 将进行全面的调查以找出事故发生的原因。 
 [ + that ] Investigators needed several months to work out that a fraud had been committed. 调查人员需要几个月的时间才能查出欺诈行为。 
 - More examples
 - I couldn't work out what was going on.
 - We're trying to work out how to finish the project.
 - I couldn't work out what his expression meant.