Spotting a circular shift between two plotted DFT-length sequences

When a DSP homework shows x[n] and y[n] as stem plots and asks for Y[k] in terms of X[k], test every circular rotation (np.roll(x, m) for m in 0..N-1) and also sign flips / time reversal before assuming anything else. For a length-6 pair, a 4-sample circular delay matched exactly, giving Y[k] = e^{-j2pi*4k/6} X[k] = e^{j2pi k/3} X[k]; reduce the exponent mod 2pi so the answer reads cleanly per bin.