Please let me know what my mistake is.

It looks like in line three you'd like to declare a variable as a random number between 1 and 6. Is that right?

If so, to create a random integer between 1 and any number, use:

Math.ceil(Math.random() * anyNumber )

Arriving at random integers is a bit convoluted in JavaScript. "Math.random()" chooses a random decimal number between 0 and 1. Multiplying that decimal number by "any number"—in your case, 6—creates a random decimal number between 0 and 6. "Math.ceil" rounds that decimal number up to the integer, giving you a random integer between 1 and 6.

So if your goal is to print 10 random numbers between 1 and 6, try rolling the dice like this:

var counter = 0;
while ( counter < 10 ) {
    var randNum = Math.ceil(Math.random() * 6 );
    document.write (randNum + ' ');
    counter += 1;
}

Problem of your code is here also:

while( ... ) {
    document.write (randNum + ' ');
}

In this code you are erasing content of your html page with new data. You should use additional variable to store whole data and then, after loop, write it on your page.

For example:

var htmlData = '';

while( ... ) {
   htmlData = htmlData + newData;
}

document.write(htmlData);

Do you have randomNumber defined as a function? you need to use Math.random() at some point to get a random number...