How did the space marine's primarch's die?

Not all 20 of the primarchs died.

6 are still alive as daemon primarchs: Angron, Fulgrim, Mortarion, Magnus the Red, Perturabo and Lorgar.

6 are dead, to all intents and purposes. Ferrus Manus (killed by Fulgrim), Sanguinius (killed by Horus), Horus (killed by the Emperor), Rogal Dorn (killed by Chaos marines post-heresy) Konrad Curze (allowed himself to be killed by an Imperial assassin) and Roboute Guilliman (killed by Fulgrim, frozen in stasis at the moment of death, so in effect dead).

1, Lion El'Jonson, is in some kind of coma, but it's unknown if or when he will awaken.

5 have disappeared or are unknown. Leman Russ, Corax, Vulkan and Jaghatai Khan all vanished at various points after the heresy. Alpharius was said to have been slain by Roboute Guilliman, but the veracity of the source is questionable (the Alpha Legion known to be an extremely secretive and deceptive legion) and even if he is dead his "twin brother" Omegon may still be alive.

2 are the unknown primarchs.

So 6 are alive, 6 are dead, the other 8 may or may not still be alive and one day active.