... I thought each series line should have its own resistor?

You had it right. I think @Bernard meant each string would have its own resistor, not as shown in your drawing.

Are we talking about typical LEDs here, the ones that drop about 3.4V at 20mA? Using that as an example, the resistor calculation would be:
14V – 3*(3.4) = I • R = 0.02 • R R = 3.8/0.02 = 190Ω

I used 14V because a 12V battery under charge can be that high. Better safe than sorry. But anyway the value is in line with Bernard's 150Ω.

Moving up to the next standard resistor value, I'd use at least a 220Ω resistor. In fact I'd consider and experiment with a 470Ω resistor because an LED will still be quite bright at 10mA. Worth a try, because your LEDs will last longer. If you need more light and want to use 180Ω or even the 150Ω, that's fine. I'd probably want to measure the actual current at 150Ω, to be sure I wasn't exceeding the specs of the LED.

 

You had it right. I think @Bernard meant each string would have its own resistor, not as shown in your drawing.

Are we talking about typical LEDs here, the ones that drop about 3.4V at 20mA? Using that as an example, the resistor calculation would be:
14V – 3*(3.4) = I • R = 0.02 • R R = 3.8/0.02 = 190Ω

I used 14V because a 12V battery under charge can be that high. Better safe than sorry. But anyway the value is in line with Bernard's 150Ω.

Moving up to the next standard resistor value, I'd use at least a 220Ω resistor. In fact I'd consider and experiment with a 470Ω resistor because an LED will still be quite bright at 10mA. Worth a try, because your LEDs will last longer. If you need more light and want to use 180Ω or even the 150Ω, that's fine. I'd probably want to measure the actual current at 150Ω, to be sure I wasn't exceeding the specs of the LED.

Ok thank you very much you have explained it really well, I think I am ready now to have a go at putting something together. I really do appreciate your help, and thank you to everyone else who has helped with there comments. John.....

 

I've had good battery charging characteristics using a panel directly to the DC circuit with the battery and load. But it takes the calc's, the battery/panel combination, and good knowledge of the sunlight supply characteristics too.