"欣赏" --- 大家很欣赏他的绘画作品。(His artwork is high appreciated.)
''看好'' --- (1)我看好这件衬衫了。这里的“看好”意思是“看中了,相中了”,which indicate that i like it and i will buy it.
(2)陈老师很看好他的学生们。此处”看好“指看重某人,or give someone high evaluation.
(3) 一些投资商看好今年某某公司股市。 以为前景不错或希望较大。It suggests something has a promising future and people think highly of it.