You should describe, briefly, what your truth tables are for. Don't make people guess, because that will lead to subtle miscommunications that can be hard to even detect.I've posted truth table above. Here it comes again>View attachment 114350
I'm assuming (because I am having to guess) that the left table is telling you that if the current output is the value in the Q column and you want the Q to have the value in the Q(t+1) column after the next rising clock edge, that the values of R and S need to be those given on the same line and that 'b' means that both values are acceptable. In most places this is known as a "don't care" condition and the letter 'x' is used, but use whatever your text/teacher uses and just be sure that you let people know what it means.
I'm assuming (again, having to guess) that the right table is telling me what happens to Q after the next rising clock edge given the values of the R and S inputs. Here the 'b' is more ambiguous because it's impossible to have "both" values. I think you mean that the value is unknown (though in most RSFF implementations the behavior is actually well defined -- but it is an input condition that is discouraged), in which case using '?' or 'x' is more common (in most places).
You still have this en0 input in your RSFF symbols. Is this really there? If so, what is the behavior when this is 0 and when it is 1?
While having the Truth Table (or other descriptive behavior) for the RSFF is important, it is not everything. You also need to clearly define, via Truth Table or other means, how the overall system is supposed to behave in response to all of its inputs. You finally stated (in Post #7) that C0 indicated that it should count up and that E0 indicates if it should count down. First off, how are these indicated? Does C0 indicate to count up if it is HI, or if it is LO. The signal name is meaningless in terms of implying signal polarity. Second, there are four possible combinations of the values of C0 and E0. What should happen if both are HI? If both are LO?
You also indicated that this is supposed to be asynchronous. That implies that there is no clock. This probably also means that the Co and Eo signals are strobed (e.g., a LO-HI-LO pulse on the Co line causes the counter to increment by 1). But there are several possible specifications and it is hard to help you unless you make it clear what the specifications are that you are designing to.

