Drawing State Diagrams
First design the state machine without worrying about the clk.  You have to remember something about what happened with the last 3 inputs, so at worst you are going to need 8(=2^3) states (but you can do substantially better than that.)

Once you have the state diagram, you need to choose an n-bit representation for each state.  You will store this in an n bit register.

Then you write down the truth table for the transition function.  There will be n+1 inputs (the n-bit state, and the 1 bit for X.)  There will be n output bits (representing next state.)

Then you figure out how to implement a circuit that performs the truth table.

Finally, you need to implement the output function.  This will be a circuit that is true when you are in the state where the last three bits are 110, and false otherwise.

In your final circuit you will have an n-bit clocked register, and a bunch of combinational logic.