Jack-Aku was walking on a snowy mountain in "Episode XX: Jack and The Three Monks", looking to find a portal. While the Jack half wishes to use it, the Aku half wishes to destroy it.
The part of him that is Jack is a bit scared and wants to find help, but the part that is Aku is greedy and wants to destroy everything. Due to being a mix of Jack and Aku, he constantly switches between being nice and mean.
Jack-Aku is similar to Two-Face, in how there are 2 sides: the first being good, charismatic and mild-mannered, and the second being evil, greedy and demanding. They resemble each other as well, his first half of his body being human, and the other half being a monster.