hmmm i suck at explanations. sometimes they can be used interchangeably and sometimes not. A lot of it is intuitive. I learned by hearing the usages over and over again. 那么 in that way / so very much (in that way) 这么 in this way / so very much (in this way) 多么 how / what (as an expression of emphasis) 多么新鲜的水果。 Duōme xīnxiān de shuǐguǒ! How fresh the fruit is! 多么好的主意 Duōme hǎo de zhǔyì！What a good suggestion！

zhe4 me means "so "or"so...that..." eg:i am always careless. wo3 zong3 shi4 zhe4 me cu1 xin1. she is so busy that she has no time to come home to see her family. ta1 zhe4 me mang2 yi3 zhi4 yu2 ta1 mei2 you3 shi2 jian1 hui2 jia1 kan4 wang4 jia1 ren2. na4 me also means "so " or"so...that" , u can use it like "zhe4 me4" they have almost no difference. it also can be used in above sentenses. sometimes,it can be used as adv. eg:since he is in trouble now,wo need to lend him a helping hand. ji4 ran2 ta1 chu3 jing4 jian1 nan2,na4 me wo3 men2 xu1 yao2 bang1 ta1 yi4 ba3. duo1 me means "how" eg: no matter how difficult it is ,wo must stick it. wu2 lun4 duo1 me kun4 nan2 ,wo3 men2 dou1 bi4 xu1 jian1 chi2 xia4 qu4 do u understand?

zhe me 1) Indicates the degree, manner, nature, etc. zhe4 hu2 zhe4 me shen1=this lake is so deep. 2)like that. zhe4 zuo1 zi yuan2 lai2 jiu4 zhe me fang4 3)this way ta1 ying1 gai1 zhe me zuo4=he should do this way 4)such zhe me zhao1 --------------------------------------------------------------------　 na me 1)thus ta1 ji4 ran2 bu2 lai2,na me wo2 ye3 hui2 qu4 le=Since he has not come, then I have to go back 2)Indicates the degree, number, etc. na me duo1 hai2 zi.=so many kids -------------------------------------------------------------------------- duo me 1)use in Interrogative, exclamatory 2)Refers to the degree of deep ------------------------------------------------------------------------- ps: notice the 'zhe' and 'na'. zhe:Refer to more recent time, place or thing, and "that"relative.

Look not to understand