How does paxos algorithm handle partial failures of accept messages?
The paper's specification for the phase 2(b) of the algorithm, which is how an acceptor responds to an accept message is the following:


  If an acceptor receives an accept request for a proposal numbered n,
  it accepts the proposal unless it has already responded to a prepare
  request having a number greater than n.


This means that acceptors are allowed to accept multiple proposals (even with different values) in a single instance of Paxos, as long as they have not responded to a prepare request with a number greater than the number of the accept message. As a result, even after the last row of the example, a proposer could bring the system to an agreement, by making some of the nodes accept a different value.

For example, the proposer could send a subsequent prepare(6) message to nodes 1,2,5,6, followed by an accept(6, B) that reaches everyone, thus reaching a majority and concluding the consensus. The important thing to note is that after this point, it's impossible to form a majority with a different value, because any potential majority quorum would contain at least one node returning (6, B) during the prepare phase.