The iPod 6-pin–to–4-pin FireWire Adapter was specifically included with the iPod Generation 3 (Dock Connector) to make it compatible with Windows computers. According to the iPod User’s Guide:
To use iPod with a Windows PC, you must have:
• A Windows PC with 500 MHz or higher processor speed
• Windows 2000 with Service Pack 4 or later, or Windows XP Home or Professional
• iTunes 4.2 or later (iTunes is included on the iPod CD). To be sure you have the latest version of iTunes, go to www.apple.com/itunes.
• iPod software (included on the iPod CD)
• Built-in FireWire or a FireWire card installed, or built-in USB 2.0 or a USB 2.0 card and the optional iPod Dock Connector to USB 2.0 + FireWire Cable
Although all Mac computers at the time had a 6-pin FireWire port built in, Windows computers had many different possible ports. For Windows, the iPod Generation 3 could support three connectors: USB port (USB 2.0 recommended), 6-pin FireWire 400 port (IEEE 1394), or 4-pin FireWire 400 port (with included adapter).
The 4-pin FireWire adapter only supported data transfer, it could not charge the iPod.
Source: Apple (manual, Identify your iPod model)