Appreciate is followed by the gerund alone when the gerund refers to the subject of a clause, but it is followed by a possessive adjective + the gerund when the gerund does not refer to the subject. Appreciate can also be followed by a noun.
- I appreciate having time off work.
- I appreciate your giving me time off work.
- I appreciate time off work.
- We appreciate eating chocolate cake.
- We appreciate his eating our chocolate cake.
- We appreciate chocolate cake.