~을/를 잘 하다 – to do well, to be good at 
~을/를 못 하다 – to be bad at  

노래를 잘 하다 =  to be good at singing, to sing well. 
요리를 못 하다 = to be poor at cooking, to cook poorly.  
 
못 하다 = can’t do  
잘 못 하다 = can’t do well

수영을 잘 하다 = to be good at swimming 
수영을 못 하다 = to be poor at swimming OR unable to swim. 
수영을 잘 못 하다 = to not be good at swimming.   

잘 달리다 = to run well, to be good at running 
잘 쓰다 = to write well, to be good at writing. 
(sometimes this is not clear, so add a noun to the phrase.) 
다리기를 잘 하다 = to do running well.  
글씨를 잘 쓰다 = (writing/letters) well (to write/use) 

저는 노래를 잘 못 해요 = I can’t sing well.  
제 친구는 수영을 잘 해요 = My friend is good at swimming. 
저는 퍼즐을 잘 풀어요. = I am good at solving puzzles. 
저는 글씨를 잘 못 써요. = my handwriting is not good.  
저는 글을 잘 못 써요. = I’m not good at writing. 
매운 거 잘 먹어요? = are you good at eating spicy food?    
너 요리 잘해? = are you good at cooking?
나는 노래를 못해요 = I am bad at singing.