The piece
The full title is longer: Fröhlicher Landmann, von der Arbeit zurückkehrend, the cheerful peasant coming home from work. First you hear him singing low down in the left hand, a straightforward F major tune marked Frisch und kräftig (fresh and vigorous). In the second half the tune reaches the right hand as well: both hands sing it together, a tenth apart, with chords slipped in between.
The left hand carries the tune with weight, like a full, low voice. The right hand fits chords between the melody notes, always after an eighth rest, and they must be short and clearly lighter. That offset is the first trap, because the right hand tends to lock onto the left and land with it. Count the eighths out loud at first. In the second part the right hand keeps its chords while also singing the top line: share the weight between the outer fingers, which sing, and the thumb, which accompanies. Practising hands separately is mostly a way to hear those two roles clearly here.