In a mod-6 counter you are using a 3-bit counter that actually has 8 states. However, when the counter reaches the seventh state (Q2 = 1, Q1 = 1, Q0 = 0), you force the counter to return to the state (Q2 = 0, Q1 = 0, Q0 = 0)...
For this you use an AND gate, whose output is connected with the RESET inputs of the flip-flops...
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With the circuit shown you realize easily that the counter now produces only 6 states...
You find a mod-6 counter in many applications where time is "counted".
In addition you find in many applications a mod-10 counter...