Create an array of Buttons to represent your button layout, replace MyButton with your button type:
MyButton[,] buttons = new MyButton[4,4];
Whenever a button is clicked, find it in your array (or store the location in the Tag property or your own custom properties, and use offsets to select the other ones, like this:
int x = clickedButton.Row;
int y = clickedButton.Column;
if (x > 0) MyButton[x-1,y].ForegroundColor = ...;
if (x < 3) MyButton[x+1,y].ForegroundColor = ...;
if (y > 0) MyButton[x,y-1].ForegroundColor = ...;
if (y < 3) MyButton[x,y+1].ForegroundColor = ...;