Translation:I like pants more than skirts.
According to this thread: https://www.japan-guide.com/forum/quereadisplay.html?0+81156
"... no hou ga" literally means "the direction of...," or "the side of... (in the sense of "this side vs. the other side")" pointing at one thing/person over the other in comparison.
When it's obvious that the sentence is making a comparison between two things, のほう can often be omitted without changing the meaning.
Using 「方」 and 「よる」 http://www.guidetojapanese.org/learn/grammar/comparison
〜のよ (~no yo).
Using this combination of ending particles can make you sound pretty feminine. If after a na-adjective you can add a “na” before “no yo”
- I like that.
Rarely I’ve heard this appreciated as “~n yo”. (〜んよ).
This sentence pattern is used when there are only two options. HOU could be translated something like "the side of." So here you have the side of pants and the side of a skirt and you have to pick a side. You can leave the NO HOU out of the sentence without changing the meaning. In fact, I disagree with their English translation. Using NO HOU creates something more along the lines of "I prefer," which is a little less in degree than "I like." There is a general rule in Japanese that longer equals more polite. Little extras are often added to a sentence simply to lighten or soften the tone a bit. Saying "I like pants more than skirts" is fine, but saying "I prefer (the option of) pants to that of skirts" is a little less decisive or clear cut and, therefore, preferable because it is less likely to offend a listener who might feel the other way. It's a very small difference.
Why are the majority of these example sentences female centric? As a male learner, I rarely have a need to go shopping for blouses, skirts and pretty diamonds. In addition Duo needs to recognize that Japanese spoken by men and Japanese spoken by women has significant and potetially embarrassing distinctions.