Answer: This depends on the instrument: Fp means the note should be attacked forte and then immediately go to piano. On a stringed or wind instrument that's not hard to accomplish, but this might be piano music you're telling me about. Naturally you can't "take back" the speed with which you strike that key once you've struck it, but you can at least make sure that the following 8th note is quiet. You could consider this to be about the same effect as an accent mark on the quarter note.

If a pianist is skilled enough in use of the damper pedal it is possible to slightly damp a note immediately after striking, without actually stopping the sound. And I saw a master class once in which Karl Ulrich Schnabel insisted he could create a vibrato effect (apparently meaning a volume vibrato) by shaking his hand after depressing a key. He pretty much had the audience hypnotized into believing this (" There! Can you hear it?!" "Yes! Yes!"). If he was right then he was controlling volume after striking the note (controlling pitch on the piano would be even more unlikely!). Personally I didn't hear it.

But that brings up a related Schnabel remark: he said that a note following a long note must be played a little softer unless one means to crescendo. If you think about it this makes perfect sense at least with a pair of notes, since the piano's sound dies away over the course of a long note. And it applies perfectly to the example you cite: the syncopated quarter note is emphasized, and in order to maintain its emphasis the following 8th must be struck much more softly.