Yama/Ganapati is lord of the 4th lunar day, which is good for the destruction of one's enemies, the removal of obstacles, and acts of combat.
Shukla Chaturthi is the name for the 4th Tithi (lunar day). It's nature is Khala Prada, which can be interpreted as "cruel, wicked or bad in nature". It's good for using weapons, keeping arms, killing of enemies, arresting actions, poisoning, igniting fire, Atharva Vidya, works related to electricity. No Manglik (auspicious) works should be done as they get destroyed. Ganesha (Ganapati) is Devata which rules the 4th Tithi (referring to Muhurta Chintamani and Poorva Kalamrita), which is good for the destruction of one's enemies, the removal of obstacles and acts of combat. As per Brihat Samhita, Shukla Chaturthi is ruled by Yama and all actions done in respect of Yama are acceptable.