The Anet A8 uses a simple LCD with 5 buttons, the problem is that the buttons do not use digital pin signals, instead analog pins are used. Based on the pressed button, with corresponding resistance the firmware knows which button is pressed. The RAMPS smart adapter uses digital pins, so **the Anet LCD is not compatible with the smart adapter** , you may wan't to opt for a cheap Chinese 12864 LCD smart controller, they are about $8, they are compatible.
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The topic Connecting (Anet A8) 2004 display to MKS GEN L shows you to hook up the Anet A8 LCD to a RAMPS board. You **do not use the smart adapter** , instead **you use AUX2**. You only have to change 2 wires (interchange them on AUX2) and you will be able to use the display. The reason you cannot use the smart adapter is that the 5 button display requires analog pins, which are not available on the smart adapter, but are available on the AUX2 header.