6x^2 where x = 1/3 is the same as 6 times (1/3)^2. (1/3)^2 = (1^2) / (3^2) = (1/9) therefore 6 times (1/9) = 6/9 which reduces to 2/3. Remember the exponent only applies to x and not 6x since 6x isn't in parentheses..
You would start off by consulting BEDMAS:
Brackets
Exponents
Division
Multiplication
Addition
Subtraction
As there is nothing you can do to "6x2", you would go on to the next step of replacing "x" with "1/3", giving you:
6(1/3)2
Now you can do something with this. If you look at bedmas, what it seems to be telling you to do is to simplify 1/3 (solve the brackets), but that would give you a big weird approximate number like "0.33333333333333333 . . . ". So instead you should leave it as a fraction, which will make it easier for you later in the equation. Besides, most schools prefer students to not simplify fractions, as it works counter-intuitive to the skills they are trying to teach them. Moving on, the next step of bedmas is exponents. In this equation, it's the "(1/3)" that's being squared; you would not square the six, and the six would not multiply by "(1/3)", as multiplication comes after exponents when it is outside of brackets. To square a fraction you square the top and the bottom, and in this example that would give you "(12/32)", which you can simplify to "(1/9)". To put that into an equation, that would be:
6(1/3)2
= 6(12/32)
= 6(1/9)
Which, because any number next to a bracket multiplies by the number in that bracket, you can simplify further to:
6 * 1 / 9
And that gives you:
6/9
After taking time you can never get back to chuckle at "69", you would either simplify completely (divide 6 by 9), or simplify to a lowest numerator and denominator by factoring. The foolproof method for factoring is to break down the numerator and denominator to their prime factors(any positive integer(whole number) that cannot be divided to any other integer to make another integer except by one and itself). This may be easier to demonstrate:
6/9
= (3*2)/(3*3)
Then look for like terms and cross them out to replace them with ones:
( 3 *2)/( 3 *3)
= (1*2)/(1*3)
And then you solve:
(1*2)/(1*3)
= 2/3
And there you go, your final answer.