Sony BRAVIA 2 II LED TV game mode, 120 Hz or VRR is not working

The checks in more detail

The Motionflow XR 240 figure on the box is a measure of motion interpolation and backlight techniques, not a real 240 hertz refresh. The TV still makes a good gaming screen at 60 hertz. Use Game Mode to cut input lag: set the HDMI input to Game, or let the TV switch automatically when a console is detected, and the processing is reduced for a more responsive picture. Turn off Motionflow and other motion processing in Game Mode, since it adds delay.

Make sure the console is set to output 4K at 60 hertz with HDR where available, and that Dolby Vision is on where the console and game support it, since the TV does support Dolby Vision. Use a high-speed HDMI cable on the HDMI port that supports 4K HDR; the manual marks which ports carry the enhanced format, and the setting for the input is called HDMI Signal Format, to be set to Enhanced. Check the console. Tell the console that the TV supports 60 hertz and not 120, or turn off 120 hertz and VRR in the console's video settings,

so it does not try a mode the TV lacks and show a black screen or a message. If a game offers a performance mode at 60 frames per second, choose it on this TV. If you want 120 hertz and VRR, you need a TV with HDMI 2.1, for example Sony's higher models or another brand, and a console and a certified cable. Update the TV software through Settings, System, About. If your console says that it cannot detect a 120 hertz display, that is the correct outcome. Contact Sony with the model number if a 60 hertz picture is wrong.