I'm attempting to tease apart what you mean by '4000 years ago'. Because advanced as china has been for much of its rich history, no people in 2000 bc possessed the naval technology and means for travel over water capable of that kind of journey. There is however an emerging ancient historical field that is recognising far flung travel across Eurasia in ancient times; the west and east were discoverable to each other over land. Study of the silk roads for instance reveals much exchange between the west and east.

But to answer the question as I think it's meant, as in, by the renaissance, why did China not seek to explore Europe and the Americas, I think it's predominantly to with trade. Europeans were largely seeking a naval trade route with India, and it is why the West Indies were mistakenly named as such. Europeans were motivated by economic competition which was a necessity in a geo-politically divided Europe, one that now had to swallow Ottoman monopolies on trade in the east.

China on the other hand was not so nearly desperate. It was located as it were, on the more resourceful side of the globe, it had much less need for exploration.

There are arguments that point towards an 'oriental mindset' that prohibited exploration and industrialism. That the Chinese were insular. I don't believe this to be the case, though you are free to make your own mind up. In my opinion, nobody with enough money would pay for or themselves venture on a journey that may be fatal in search for greener pastures when there's pastures green at home. China had spice, silk, tropical luxuries, ect.

Inevitable some Chinese did explore, for instance: Faxian, and Zheng He.