Congrats...the '008 is a killer little unit. I have one myself, firmware-updated to '008ex. LOVE it. Works like the bigger ones, sounds every bit as good.
Here's my nickel's worth on your question:
First off - before getting into the connectivity - I strongly recommend against using computer speakers as output for your '008. They are simply not of adequate sonic quality to represent what you record, and (depending on your expectations) you are sure to be disappointed. In fact, you'd be better off with a decent pair of headphones. But I'd be inclined to recommend a small pair of powered monitors - you can get a pair of very compact, quality-sounding ones in 3-5" range for well under US$100. Those would be no bigger (possibly SMALLER) than your intended computer speaker solution, and probably sound WAY better. Prowl Reverb dot com.
That said - if 'puter speakers is the route you wanna/gotta go:
Most powered stereo computer speaker sets have a SINGLE TRS 1/8" plug. You would connect that to the [PHONES] connector.
OR - if you prefer to/must use the [LINE OUT] connectors - you'll need the adapter you described. BUT: having never tried this method (why would I?) - I'm not able to say whether the line-level output is a good match for the hookup you wanna do.
But at least you've got a couple options.
