Controlling RGB LED with two buttons.

I think the OP wants a simpler way than analog write. Aqua is Blue+Green, Yellow = Red+Green, and Purple=Red+Blue.

Something like this might suffice (not compiled or tested):

const int BluePin = 9;
const int GreenPin = 10;
const int RedPin = 11;
const int IncrementButton = 2;
int colormode;

void setup(){
  pinMode (BluePin, OUTPUT);
  pinMode (GreenPin, OUTPUT);
  pinMode (RedPin, OUTPUT);
  pinMode (Incrementbutton, INPUT);
}

void loop(){
  switch (colormode){
    case 1: //white
    digitalWrite(BluePin, HIGH);
    digitalWrite(GreenPin, HIGH); 
    digitalWrite(RedPin, HIGH);
    break;
    
    case 2: //red
    digitalWrite(BluePin, LOW);
    digitalWrite(GreenPin, LOW); 
    digitalWrite(RedPin, HIGH);
    break;    

...
...


    case 5: //aqua
    digitalWrite(BluePin, HIGH);
    digitalWrite(GreenPin, LOW); 
    digitalWrite(RedPin, HIGH);
    break;

    case 6: //yellow
    digitalWrite(BluePin, HIGH);
    digitalWrite(GreenPin, HIGH); 
    digitalWrite(RedPin, LOW);
    break;

...
...

ect...
}