Phase-transfer catalysis is often used to enhance the Suzuki reaction. An explanation of how quat salts likely help the Suzuki reaction was provided by Dr. Peter Wuts shown here: http://phasetransfercatalysis.com/ptc_tip/alternative-explanation-for-ptc-suzuki/.
Tetrabutylammonium bromide is used as the phase-transfer catalyst in the reaction shown in the diagram as well as in other PTC Suzuki reactions we have reported in the past such as http://phasetransfercatalysis.com/ptc_reaction/consecutive-ptc-reactions-suzuki-demethylation-etherification/.
In contrast, we have reported that the more organophilic Aliquat 336 has been used more often for PTC Suzuki reactions. See for example: http://phasetransfercatalysis.com/ptc_reaction/ptc-suzuki/, http://phasetransfercatalysis.com/ptc_reaction/ptc-suzuki-2/, http://phasetransfercatalysis.com/ptc_reaction/ptc-suzuki-3/, http://phasetransfercatalysis.com/ptc_tip/ptc-suzuki-for-polymers/ and http://phasetransfercatalysis.com/ptc_tip/use-of-aliquat-336-for-palladium-co-catalyzed-ptc-reactions/.
Toluene is most often used as the solvent in PTC-Suzuki applications. The reaction shown in the diagram used DMSO as the solvent.