HELP Question

Top solution is better, but you still want a resistor in series. Lower solution is not a good idea: small tolerances of forward voltages between LEDs will result in a considerable spread of current. Dimension resistor at top like this: add up all LED forward voltages, subtract sum from supply voltage, then divide by desired current. The lower the voltage over the resistor, the less power is wasted.

Depends on the application, both options may be viable.

Here is why second approach is not recommended, even though incompetent lenzsux calls it "viable": http://everycircuit.com/circuit/5192853928804352

This is a really good question. Why is the LEDs in series better than the LEDs in parallel. If one of the LEDs in series fails then the whole circuit fails, but with the LEDs in parallel, the rest of the circuit will still work. I would really like to understand this.

"Break" one of the LEDs when they are in parallel, without each LED having its own resistor, by removing or disconnecting the LED, then look how it affects current through the remaining LEDs. Think about how that will affect the life time of remaining LEDs. The other problem with Vf tolerances I have already demonstrated in the link above. When connecting LEDs in parallel, it boils down to giving each LED it's own resistor, while LEDs in series can do with a single resistor for all. As supply voltages are often much higher than a single LED Vf, voltage drop over resistor is lower too, resulting in better efficiency (less power used to heat up the resistors)

Additional thought re "failing": depends on how a single LED fails: in case of it shortcircuiting, the LEDs in series will continue to operate (albeit at increased current), while when parallel without individual resistors, the shorted LED shorts out all other LEDs.

For a fixed 12V supply, I'd most likely use a setup like this: http://everycircuit.com/circuit/5564365982662656

Thanks all for the input.

You're welcome.