ok how do i challenge some one for private match ?

You need to add the one you want to challenge as a friend. you can either add your friend from the ranking list or by the player ID, which you can find yours in the friends section. It doesn't work by player name since there can be multiple players with the same name, so the devs don't use that option.

Second, both of you have to be online at supermechs, in the friends section, your online friends will have a green background, while others have black background. If you select one of them though, that friend will be highlighted with a yellowish background, regardless of the friend being online or not.

Also when you select your friend, if (s)he is online,an "invite to battle" button will appear at the bottom, alongside with the "delete friend" button. If not, only the delete friend button will appear.

I hope i could help

yes