If you have a liking for something or someone, you like them.
She had a liking for good clothes.
她喜欢好衣服。
He bought me CDs to encourage my liking for music.
他给我买了CD来鼓励我对音乐的爱好。
for someone's liking
If something is, for example, too fast for your liking, you would prefer it to be slower. If it is not fast enough for your liking, you would prefer it to be faster.
He had become too powerful for their liking.
对于他们来说,他已变得过于强大。
to someone's liking
If something is to your liking, it suits your interests, tastes, or wishes.
London was more to his liking than Rome.
伦敦比罗马更合他的意。