On the M20 engine, the exhaust manifold consists of two parts, i.e., two large castings.
The passenger side of the cylinder head has several studs sticking out of it on the exhaust side. The holes in the exhaust manifold parts slide onto these studs. Then, some 12 mm nuts press the exhaust manifold castings against the cylinder head.
There is a 12 mm nut on each of two two diagonal sides, for each of the six exhaust gas outlets, for a total of twelve such nuts. These tend to be tight, so I hit them with PB Blaster. This is an intense penetrating oil that’s similar to WD-40. It makes rusted nuts easier to remove. I used a 12 mm ring wrench or a 12 mm socket on each of these. I found it possible to get all 12 nuts off without having to lie underneath the car.
The connection to the exhaust downpipe uses three 14 mm nuts for each of the two castings, for a total of six. These also got a thorough soak with some PB Blaster.
Using a ring wrench, and prying it with a couple of extensions, I was able to remove five of the six nuts. The last nut stripped, so I lay underneath the car and hammered a 14 mm socket and extension onto the nut from below, and after that, it was easy to remove that last nut and pull the manifold casting up and away.