people's awareness of （how persisitent and devastating non-biodegradable trash can be to our environment and our descendants）should be heightened.
看我的括号内的内容就明白了,括号内的整句话都是修饰前面的awareness.
而括号内的这句话其实是how sth can be句式,转换过来就成了sth can be how（某事能如何）.后面在再加不定式,表示对象.