Wow 8 years Lin, without pruning it is amazing. My first plumeria was in 2010 but I trimmed it almost every other year, mine looks like it has less branches than yours.
with Hetty and Ken's visual presentation of where to cut. Important thing is once you have the cuttings...let it callous for a few days before you plant the cuttings in a mixture of perlite and soil. Water thoroughly once and don't water them again until new leaves are sprouting. (Although in our area being so hot. I've been leaving my newly planted cuttings on my partly shade walk way and let nature take care of it. They are in terracotta pots so even if they get rained on they drain fast and the sun dries the soil fast.)