How to change color of a panel with generated color from red , green and blue button click

All you'd need to do would be to set the BackColor.

private void button2_Click(object sender, EventArgs e)
{
    panel1.BackColor = Color.Yellow;
}

private void button3_Click(object sender, EventArgs e)
{
    panel1.BackColor = Color.Red;
}

If you want to change color with clicks on buttons then
connect these event handlers to each button's Clicked event.

private void btnRed_Clicked(object sender, EventArgs e)
{
   panel.BackColor = Colors.Red;
}

private void btnGreen_Clicked(object sender, EventArgs e)
{
   panel.BackColor = Colors.Green;
}

private void btnBlue_Clicked(object sender, EventArgs e)
{
   panel.BackColor = Colors.Blue;
}

In order to change color with combination of buttons I suggest to replace buttons with checkBoxes and add this event handler to each checkBox's Checked event.

void checkBox_Checked(object sender, EventArgs e)
{
  int state = 0;
  if(btnRed.Checked)
  {
   //001
    state += 1;
  }

  if(btnGreen.Checked)
  {
    //010
    state += 2;
  }

  if(btnBlue.Checked)
  {
    //100
    state += 4;
  }
 
  switch(state)
  {
    //red
    case 1:
       panel.BackColor = Colors.Red;
       break;
    //green
    case 2:
       panel.BackColor = Colors.Green;
       break;
    //blue
    case 4:
       panel.BackColor = Colors.Red;
       break;
    //red + green
    case 3:
        //whatever you think is appropriate 
        break;
    //
    //code for other combinations goes here
    //

    default:
        panel.BackColor = SystemColors.Control;
  }
}