zěnme 怎么 and zěnmeyàng 怎么样 can both means ‘how to’, as question words to ask methods.
While they are distinct when asking reasons and features of things. To be precise, zěnme 怎么 can be used to ask reasons with the meaning of ‘why’ while zěnmeyàng 怎么样 can be used to ask feature and states of people or things, with the meaning of ‘how about’. For example,
1)你怎么不喜欢他?
Nǐ zěnme bùxǐhuan tā
You why don’t like him
‘Why you don’t like him?’
2)这个人怎么样?
Zhègè rén zěnmeyàng?
This person how about
‘How about this person?’