A subconscious projection is when a person denies his or her own thoughts and emotions and atrributes them to other people. So Carl Jung is saying that he wants his Valentine to do this for him.
The anima archtype is basically the female representation within the male. Carl Jung thought that the female represented the man's emotions, his nurturing and caring quality, forgiveness, his sense of what is natural and his connection with nature, its cycles and drives.
It is also the archetype that is responsible for much of our love life: We are always looking for our other half in members of the opposite sex. When we fall in love at first sight, then we have found someone that "fills" our anima (or animus for girls) archetype particularly well!
Ol Carl, in his very word-heavy way, just wants his Valentine to be his soul mate. :)
