Well, serial/parallel is just how they're wired, you can arrange them any way you like. Stripboard is gonna lend itself to parallel more easily than series, but if you're willing to cut tracks then you should be able to work it all out. Maybe you'll need a couple jumpers.
well, stripboard makes it easy to wire everything in one big parallel combination. just use two tracks, everything you connect will be in parallel. For series, you'll need to have the LEDs connected anode to cathode. So you could make several breaks in the tracks thusly Code: + 12V o|o o|o o|o o|o | | | | | | | _ _ _ _ _ _ / v ^ v ^ v ^ \ - - - - - - / | | | | | | | o o|o o|o o|o o gnd in order to get a series string of six together. Just use the first and last columns as tie points to connect your strings in parallel to each other. That would be two adjacent track on the stripboard, I drew the circuit symbols in which pushes them apart, but you'd need to have wires running the length of the strip to tie your supply and ground points together in parallel fashion.
Yes - that's how I thought to connect the initial in-series LEDs. I'd assumed that I could connect the +ve lead at the start of the upper track (upper left as you have drawn it) and the -ve to the end of the lower track (far lower right). Or would I also need to connect another +ve lead to the far right end of the upper track?