@adamliu If you're serious about doing your assignment, don't wait until the last minute because the speed at which guidance will be offered will be limited by your efforts.
It would be helpful if you told us what wasn't working.
You can't use RCO from the S1 counter to enable the S10 counter because RCO will never go HIGH.
74163 has synchronous clear, so you're decode logic is wrong.
Why are you connecting the outputs from the S1 counter to the S10 counter load inputs? You never load anything.
It appears that you've been working on this problem for 11 days. When is the assignment due? Why are you being asked to use binary counters instead of decade? Using decade for S1 would simplify the logic (slightly).
I'll give you a hint. Since the clear function on 74163 counters is synchronous, you can't connect the clocks in parallel. Can you understand why?
If you'd post the complete text for the problem, as I asked you in your other thread, we might be able to understand why you're using binary counters instead of decade.
EDIT: Threads have just been combined.
Kudos to you for having a schematic that isn't unnecessarily difficult to read.