Note that an alternative to using the 'find' method is to use the 'contains' method to determine if the LinkedList contains a particular item. The reason we would favour the 'contains' method is that there's some chance that we might change the signature of the private helper method 'find' - if we implement it using iteration rather than recursion, for example, we could change the parameters - or we might even choose to eliminate this private helper method completely. If we were to make such modifications, your containsAll method will break. However, there is far less chance that we would modify the signature of the public 'contains' method, as doing so would break client code that makes use of this method (and there's potentially a huge amount of code that would do so).
I recommend that you add some tests to check whether or not your method below meets the given specification. Actually, let me state that more strongly: you absolutely must write some tests :-)
Paul