[INFO] JavaFinder.parseWinJavaVersion:137: Java Version: 1.7.0_51 sorted as: 1.7.0_51 32 Bit Java at : C:\Program Files (x86)\Java\jre7\bin\java.exe
You have a 64bit system please use the 64bit version of Java so you can allocate more than 1.5GB in the launcher most of the new packs run best with between 2 and 5GB allocated.
[ERROR] LauncherConsole$OutputOverride.write:89: From Console: java.io.IOException: Cannot run program "C:\Program Files (x86)\Java\jre7\bin\javaw.exe" (in directory "C:\Users\Dallas\Desktop\FTB Multiplayer\TechWorld2\minecraft"): CreateProcess error=267, The directory name is invalid
The above error makes no sense unless maybe your antivirus is not allowing this to happen. The FTB folder appears to be in the correct location, on your desktop.
Please follow the
basic troubleshooting guide to ensure Java is not the problem and get the 64bit version. After that you might want to try to add the FTB folder, the one on your desktop, to the exceptions list of your antivirus program if you continue to experiencing problems after following the basic troubleshooting guide.