Help fixing exhuast manifold on my integra engine head?

Aside from drilling and tapping the hole to accept a larger bolt and the exhaust manifold as well...you could also try installing a solid Helicoil type of repair like they use for spark plug holes....not sure if one is available for the size you need. A regular Helicoil may also work if the hole is not in a water jacket. Most parts stores sell the kits for Helicoils in various sizes.

http://www.helicoil.com/products/helicoil.asp

The hole has been stripped of the threads. You could drill out the manifold itself to accept a larger bolt, but you would also have to re-thread the head bolt hole. It is possible that the head bolt hole cannot be enlarged due to close tolerances on water ducts through the head for coolant to pass through. You might need a new head. The only way to know is to try. You should bring it to an experienced mechanic for this sort of maintenance. If you screw it up it could be very expensive.

I had that problem with my 95 and what I did was taped the hole and put a bigger bolt in.

You could get a thread and die kit and re-thread the hole to use a bigger bolt being careful not to crack the block.