I have a 1989 acura integra 24 valve V6 2700 engine that is hard to start an when its started black smoke come out of the tail pipe.... WHAT IS IT?

I have to disagree with Darth Continent. Blue smoke usually indicates burning oil. White smoke indicates water in the cylinder. Black smoke usually indicates that the fuel mixture is too rich. Look for a dirty air filter first. That can block availably air to the carbeurator or throttle body. If that isn't it, look for something wrong in the carbeurator, throttle body or injectors. In a car with a carbeurator, it usually indicates problems with a float or needle valve. I'm not as familiar with a fuel injected engine.

The '89 Integra came with a 16 valve 1.6L 4-cylinder engine. You probably have an Acura Legend unless somebody swapped a V6 into the car.
Black smoke means that you are running rich (ie, too much fuel). It could be caused by a bad injector, computer, fuel pump, or possibly a bad O2 sensor. Has your fuel economy dropped?
If the smoke has a blue tint to it then you are burning oil and have bad piston rings or valve seals.

Black smoke probably indicates the engine is burning oil, so you might have an oil leak or a bad gasket somewhere.

Its burning rich.
When its hard to start it could be:
Low Battery Charge
Clogged fuel injectors
Worn spark plugs
Bad spark plug wires
Timing could be off
Worn starter pinion gear or ring gear on fly wheel
Cylinder head leak
Worn piston rings
Worn valve seats causing the combustion chamber to not seal adequatly
Weak primary ignition system
An air leak could cause a poor means of creating vacuum in the engine
(These conditions may vary to a certain extent depending on the severity of the issue.)
Just because no one experienced it doesnt mean that it is not possible.