I think 12 plates will be inadequate. Aim for 14 - 16 at least. Opt for a slightly bigger system than your current needs if you want to have 0 bills or future proof your setup. Consider the fact that you might need to shift to electric geysers / electric home heating as gas is dissappearing fast.
A rough calculation is that a 6kw setup will generate 30 - 35 units during the summer. This will go down in winters.
In order to calculate your ROI, take your year round bills and factor in the following:
Off peak units are evenly exchanged for units exported to the grid. Plug in values of your 6kw units here and see if they meet your off peak units or not. If not, you'll be paying a differential for those units.
Peak units are charged at 37rs / unit here in khi. These need to be paid in full and there is no exchange. To simplify, 2 units of off peak excess units exported will enable you to nullify this. If you have a smaller system with no excess units, you'll need to pay this in entirety.
With electricity unit charge increasing, this will further reduce your ROI. Installing solar is not only financially feasible, it provides comfort and peace of mind regarding the future also. For me personally it has drastically improved my standard of living here in PK.
Hope this helps, good luck.