There are no mainstream 2x2 motorcycles made today despite a few of the big manufacturers playing with the idea. I think it was Yrjo Vesterinen who experimented with a converted trials bike for competitive use back in the 80's but despite having better traction it came with a weight penalty and sapped excessive power from the engine and was found to be less nimble and too unwieldly for serious competition. Apart from the farm type 2 wheelers like the one in the pic, fact is, you just don't need 2wd on a dirt bike 99% of the time and for the odd time it would help, the added cost/complexity/weight just isn't worth it.