how many bit binary counter?
It is not a full digital counter, as it has 4 bits which may hold up to 16 different patterns but only 4 are used.

What your instructor attempted to do was to take a 2-bit binary counter using two flipflops, then use a superfluous amount of NOT gates together with some ANDs to let each AND gate react to exactly one pattern out of the possible four (in essence a binary decoder).

What you are really looking at is a shift register. You can construct it using 4 edge-triggered flipflops, where the output of each flipflop is connected to the iput of the next, and the last one is looped back to the first. Each transition of the 'clock' signal will then move the contents of each flipflop to the next. Getting those flipflops in the initial '1000' state requires some additional circuitry.