I cannot find the Polygon Neighbors tool. I have searched for it as I usually do and I have also browsed the proximity toolset but it is not there. The other Tools, e.g. Buffer and Near are there and work fine.
Here is a screenshot:
This tool is available only since 10.1, you've indicated that you are on 10.0. ArcGIS 10.0 Help page is here.
Your option is to upgrade to 10.1 or later or find 10.0 system and custom tools that could do a similar thing without using this 10.1 tool. I bet you can do this in ArcPy even in 10.0.
So it's actually very simple, as suggested by @FelixIP:
Spatial join one to many in ModelBuilder, then export the resulting table to excel and create a pivot table to summarise values of the B polygons.