You don't use the correct syntax. I assume you mean:

    // NeoPixel Display   
    if ((counter >=3) && (counter <=9))
    {
      strip.setPixelColor(0, 255, 0, 0); //set pixel number 1 and set color to red
      strip.show(); //send color to pixel 1 on NeoPixel Ring  
    }
    else 
    {
      strip.setPixelColor(0, 0, 0, 0)
      strip.show();
    }

And similar for the other colors.

First you see there are a lot of occurences of calls to setPixelColor and show. We make a function of this, where the color and the red value is parameterized:

    void setPixel(int pixelNumber, int red)
    {
      strip.setPixelColor(pixelNumber, red, 0, 0);
    }


Now we can write your code as

    // NeoPixel Display   
    if ((counter >=3) && (counter <=9))
    {
      setPixel(0, 255);
    }
    else
    {
      setPixel(0, 0);
    }

    void setPixel(int pixelNumber, int red)
    {
      strip.setPixelColor(pixelNumber, red, 0, 0);
      strip.show();
    }

And similar for the other colors.

Now we get rid of the if statements. For the first color this will become:

    // NeoPixel Display   
    setPixel(0, ((counter >= 3) && (counter <= 9)) ? 255 : 0);

Combined with the other colors we get

    // NeoPixel Display   
    setPixel(0, ((counter >=  3) && (counter <=  9)) ? 255 : 0);
    setPixel(1, ((counter >= 10) && (counter <= 15)) ? 255 : 0);
    setPixel(2, ((counter >= 16) && (counter <= 21)) ? 255 : 0);

    void setPixel(int pixelNumber, int red)
    {
      strip.setPixelColor(pixelNumber, red, 0, 0);
      strip.show();
    }

However, the conditions can be simplified by adding them into the function. So we get

    // NeoPixel Display   
    setPixel(0, counter,  3,  9);
    setPixel(1, counter, 10, 15);
    setPixel(2, counter, 16, 21);

    void setPixel(int pixelNumber, int counter, int lowValue, int highValue)
    {
      strip.setPixelColor(pixelNumber, 
         ((counter >= lowValue) && (counter <= highValue)) ? 255 : 0, 
         0, 0);
      strip.show();
    }

If you need to have more checks if a value is in range you can make it a specific function. This will increase the code, but makes it easier to reuse code. So you will get:

    // NeoPixel Display   
    setPixel(0, counter,  3,  9);
    setPixel(1, counter, 10, 15);
    setPixel(2, counter, 16, 21);

    void setPixel(int pixelNumber, int counter, int lowValue, int highValue)
    {
      strip.setPixelColor(pixelNumber, 
        inRange(counter, lowValue, highValue) ? 255 : 0,
         0, 0);
      strip.show();
    }

    int inRange(int counter, int lowValue, int highValue)
    {
       return ((counter >= lowValue) && (counter <= highValue));
    }