Using Herlihy's model and definition of the wait-free hierarchy, a queue (a shared object with enqueue and dequeue) has consensus number 2, because we can initialize the queue with some value, and the first process to dequeue it "wins".
However, it is also possible to do wait-free consensus with queues that start off empty (for example, given as an assignment here, question 1).
I wasn't able to come up with the algorithm - would like help.
A hand-wave explanation: Two processors run asynchronously and communicate via shared memory, with atomic reads and writes being basic operations. We want to solve the wait free consensus problem, where each process starts with a bit value and they need to agree on one of the values, in a way that is wait free: each processor can finish in a finite number of its own steps, regardless of the progress of the others. A result says that such a task can't be done, so we include objects with more powerful operations that will allow consensus. The consensus number of an object is the number of processors in the model that can reach consensus using it. The consensus number of a queue with just enq and deq is 2. Intuitively it isn't 3 because if a processor deqs empty, it can't know which of the other processors deqd the value.