I'm going to do a very crude and unscientific calculation. It won't be valid for hermits in the mountains and such people, but maybe for standard people in a modern society it will work.

I have about 400 friends on Facebook. From what I observe, that number is about average. Besides that I have some acquaintances whom I did not add, and many relatives and older people I know who do not use Facebook. This would probably push the number of people I know to maybe 600.

I'm from Kuala Lumpur, a big city. So if we hypothesize that people from smaller places would know fewer friends, maybe we set the average at 300. So one person would be connected to 300 others.

Six degrees of separation. The first degree would be 300. Second degree would be 300 x 300, as each of your 300 friends would have 300 friends of his or her own. So the total figure as we go to the full 6 degrees would be 300 to the power of 6. This comes up to 729 x 10 to the power of 12.

729,000,000,000,000 (12 zeroes,)

Since the world population is about 6,697,254,041, according to the World Bank, this is definitely more than enough to connect the whole world.