... the lease of Queenes Colledge in Cambridge called Armsbies & Pettits ...
He presumably held properties by lease from Queens’ College, Cambridge, and he is now bequeathing the lease(s) to his son. Armsbies and Pettits will be the names of the properties.
Where did Robert Hancock live? Cambridge colleges owned vast swathes of land all over the country, so the properties may not have been in or near Cambridge.
However, Fulborne is mentioned lower down, and there is today a Pettits Close in Fulbourn (edge of Cambridge) that may relate. Someone called Armsby (or Armsbie) may have been the owner of the other property at some earlier period.