What is the distance from Wuhan terminal 2 to Hankou district?

a little bit far away, u can take the bus from the airport.

In Wuhan, Postpaid taxi is the most popular choice for public traffic except bus.
If you are comming to China for the first time. you'd better take a prepaid taxi from the airport, because seldom chinese texi or bus driver knows english. If you are not new commer or you have sb. on phone to help, then you can chose almost any type of travel methods roming inside the city as following:
(from cheap to expensive)
1\ bus (you must do preparation first, if no local Chinese accompaninist)
2\ ferry (you must do preparation first, if no local Chinese accompaninist)
3\ Authorized taxi
4\ Rent a Car (with driver better)

Caution: Don't belevie strenger's pickup beside the road. They may be operating ilegelly.

Wish you a very happy stay in China.

for any help, You are welcome to contact me (I've been in India for 5.5 years and I love this country ^_^)