Ankh is easier to tank than Fac, the only difference is that the 6th boss has a hitbox which does not belong anywhere (it is so bugged it is not even funny). There will almost always be aggro issues on fac 5, but it really is easier with a healtank IF everyone is on voice chat. If not, then it is better to do like abe said and just go in with a leecher and a normal tank as it then becomes harder to tank than ankh.
For ankh, it is recommended to either have defence gear or protection gear with glance cooldowns. The reason being that no attacks can be blocked, glanced or evaded but things like the major ward from fluid defence will trigger as if you were glanced. The same is not true for CCC or any block/evade procs. Because of this, martial discipline is more or less a must have when tanking the ankh. For a MP build, you will want Stoicism, Martial Discipline, Trial by Swords, Whippersnapper (with jones in the fast lane) and chaotic pull in your active bar. It is also recommended to bring escalation with intensity (or if you are like abe and you hate the escalation animation, blade torrent can work too) with a vexing augment on. Clearing the path is also recommended for new ankh tanks, though dancing blade can work too, but it should then be combined with elemental force etc. You also
have to bring spiral of death unless you know how to avoid Klein's waves without it. The build I have posted here:
https://www.nine-swords.com/viewtopic.php?f=41&t=7259 will work for MP, though you should instruct all DPSes and the leecher to bring flamethrowers.
For facility, you will want to bring a normal tank build if doing it with a leecher. Chaos/Blade would work very well, though you can drop some block in order to do more damage. CHaotic pull is more or less a must have, as is stoicism. Discord rising and consequence are also nice to bring expose up quickly. Clearing the path is nice for debil, but you can bring dancing blade with EF instead to do a bit more damage. Rocket jump is also strongly recommended. If you have room, you can also slot provoke to make the 5th boss easier. Be sure to have at least one impair other than chaotic pull. You can bring whippersnapper instead of rocket jump, but this will make things harder early on. Instead, I recommend telling your leecher or a DPS to bring cardiac arrest (and another impair if possible) to help you with impairs on the 5th boss. Chaotic pull is still needed, but this allows you to leave some of the impairs to the leecher or a DPS, which again makes the 5th encounter much easier, and it also frees up a slot in your active bar.
HF is best done with some evade (about 800 should do) or phys prot (as much as you can) together with block. A solid set up seems to be 800 evade, 800 block with stoicism, illusion and martial discipline/stonewalled.
HE NM is easy to tank with MP, the only difference is that you need SoH and contortionist for the entire dungeon (boss 3) or you can tell a DPS to bring an impair (cardiac arrest) for it and let them impair every other spitelance.
All the dungeons can be done by a new tank with MP with a good group, however, like abe said, HE is probably the only one where you should go straight for the MP as a tank. The others are best done after one has tanked them a few times without MP.