The flippant answer is "it depends how long you're prepared to wait". But, let's assume that you want to electrolyse a litre of water an in hour.
You've identified above that the energy needed to electrolyse one litre of water is 3.67kWh, or 3.67kW for one hour (assuming no losses in the process). So what we need is a solar system capable of delivering 3.67kW.
Let's assume that we're in a temperate latitude, that the sky is clear, and that it's the middle of the day. That should give us around a 1kW/m^2 of energy, in the form of light, reaching the ground. Decent (but not bleeding-edge) photovoltaic panels are around 15% efficient, so we'll get around 150W out of them for each square metre of area. That means that in this scenario, we'd need 24m^2 of solar panels.
That's a lot. It gets worse if you want to do this continuously, rather than as a one-off, because the average power of sunlight reaching the ground in temperate climes, including cloudy days and including nighttime, is around 250kW/m^2, one quarter of the peak value. So then you need 100m^2 of solar panels.
Let's look at it another way, and say that we have 20m^2 of rooftop available. That would mean that you produced an average of
20 x 250 x 0.15 = 750W, which works out to splitting around 5 litres of water per day.