can a 4 pin fan extension cable work with 3 pin fans?

Yes and no. Let me clarify that.

Any 4-pin fan extension cable can be used with either 3-pin or 4-pin fans. That part is not a problem.

The problem is that the female connector on the end of the extension cable is wider than a 3-pin female connector. On the Phanteks PWM Hub, the space around each output port with 3 pins is not wide enough to allow you to plug in the wider 4-pin female connector, so those cables can't fit physically, even though they would work electrically. For this purpose you really do need 3-pin fan extension cables. OR, you might be able to use the 4-pin cables IF you can custom-modify those female connectors by cutting off the area around Pin #4. (On the connector, Hole #4 is the one that is OUTSIDE the grooves that fit around the plastic tongue beside Pins 1-3 of the male connector.)

I presume that you have 3-pin fans to power and control, and that's why you want to use these cables and this Hub. SR-71 Blackbird is wrong about control of 3-pin fans, IF you meet one condition. Blackbird is correct in the sense that almost all 4-pin fan Hubs can NOT control 3-pin fans, and that is because all they do is relay the PWM signal to their fans, and 3-pn fans cannot use that signal. BUT that Phanteks PWM Hub is the one that is different! It uses the PWM signal from its host mobo fan header internally to create its own group of six 3-pin fan ports that use the older Voltage Control Mode (aka DC Mode) to control fans. That mode is the ONLY way to control 3-pin fans, and it CAN control 4-pin ones, too (although that latter is not quite ideal). So this Hub can be used with any mix of 3- and 4-pin fans.

HOWEVER, like all other Hubs, the Phanteks PWM Hub MUST have a PWM signal supplied to it on Pin #4 of the mobo fan header you plug it into. Not all mobo CHA_FAN or SYS_FAN headers to this, even if they have 4 pins! For that reason, Phanteks advises you to plug their Hub into the CPU_FAN header to ensure you get the required PWM signal, and then plug the actual CPU cooler into the Hub's white Port #1. This is not quite ideal, because it puts ALL fans (including your case ventilation fans) under control of the temperature inside the CPU chip. So, IF you can be sure that a mobo CHA_FAN or SYS_FAN header will supply the required PWM signal and you can configure that header to use the mobo's built-in temperature sensor for that header (rather than the CPU temp sensor), that's a better option. OP, post back here the maker and exact model number of your mobo, and we can figure out from its manual what its fan headers can do for this situation.