For standard lookback option payoffs:

• Floating lookback call = $S_T - S_{\min}$
• Floating lookback put = $S_{\max} - S_T$
• Fixed lookback call = $\max(S_{\max} - K, 0)$
• Fixed lookback put = $\max(K - S_{\min}, 0)$

Using the given path:

• Floating call = $8.55 - 6.79 = 1.76$
• Floating put = $39.23 - 8.55 = 30.68$
• Fixed call = $39.23 - 30.00 = 9.23$
• Fixed put = $30.00 - 6.79 = 23.21$

The highest payoff is from the floating lookback put.