Analyze why the british strategy in the middle states failed to win the war even though the british won most of the battles and captured new york and philadelphia.

I am assuming the middle states you are referring to is Virginia down to Georgia. The Americans that defended that area didn't make use of the typical military strategy that was common in Europe, in which is the line everyone up in a row and exchange shots until one side ran away. Americans instead adopted a guerilla warfare strategy, hence their whole army was never at one place at one time. 
I hope this answered your question and I apologise if I am wrong. Good luck on your assignment :)