In August, what is the bus from Beijing to Mutianyu, 936 or 864? what is the difference?

It is 936 to Mutianyu. Didn't find any information about bus 864, perhaps it is not an operating line now.

Sorry, the bus 867

thank you very much¡

It is tourism bus no. 867 that runs from Dongzhimen to Mutianyu directy. It used to be tourism bus no.936, but from this March on, it changed to tourism bus no.867.

Bus 867 available fm Mar 15th to Nov 25th, after this date, one will need to take bus 916(fast line) from Dongzhimen to Hauirou Bus Station followed by hire a mini-bus.
Can anyone tell me how much do i have to pay for the mini-bus and will it indicate specifically going to Mutianyu Great Wall or do we have to go around looking for such mini-bus?

There are many mini-buses available at Huairou Bus Station taking you to Mutianyu Great Wall. No worry. When you hear someone shouting "Great Wall", it will mean " Mutianyu''. The mini-bus ride takes about rmb30-40.