Which of the following bands may provide long-distance communications via the ionosphere's F region during the peak of the sunspot cycle?
Why The F region's maximum usable frequency depends on how strongly the sun ionizes the upper atmosphere. At the peak of the sunspot cycle the MUF can climb above 50 MHz, so the 10 meter (28 MHz) and 6 meter (50 MHz) bands can suddenly support worldwide F2-layer skip. Those two are the highest-frequency bands that regularly open this way, and only near solar maximum.
Watch out The VHF and UHF choices (1.25 meters at 222 MHz, 70 centimeters at 420 MHz, 23 centimeters at 1240 MHz) are far above any realistic MUF; signals there pass straight through the ionosphere into space, which is why they are used for satellite work.
Solar max pushes the MUF just past 50 MHz: 10 and 6 meters are the top of the skip ladder, nothing higher.