I don't understand why there is "dengan" here.
"Dengan" is not necessary here.
But it's optional? Can it generally be used with "suka"?
Yup, it's optional and it can be used with "suka".
Femmy, just wondering, is it only used with people? Does it kind of soften the statement or show some respect? (So far the examples that I've seen on Duolingo have all been with people.)
It's used with both people and objects. So you can say, "Aku suka dengan buku ini".
Why does "cara" (method) not work here?