In order to get the decimal from the fraction, you divide the numerator by the denominator. If you divide 2 by 3, you will get 0.666667. If you divide 4 by 6, the answer will also be 0.666667. It's the same, so the fractions are equivalent.
Clearly, 2/3 and 4/6 are equal. But they're not the same. For example, if you were to have 3 friends over at your house, and you wanted to eat pie. You cut the pie into sixths, and you take 4 pieces for you and your friends. Your mother comes into the kitchen and says, "2/3 of the pie is gone, who ate the pie?" You would've said, "No mom, my friends and I ate 4/6 of the pie." They're not the same because 4/6 would've been more precise.
Another example is 1/8 and 1/4; are they less than, greater than, or equal to? Let's find out.
Again, divide the numerator by the denominator. If you divide 1 by 8, you will get 0.125. If you divide 1 by 4, the answer will be 0.25. But which is more? Like I said in the beginning, you find out by comparing the place values.
As you can see, 1/8 is less than 1/4, because 1/4's tenth and hundredth places are bigger than 1/8's tenth and hundredth places. The extra 0's do not affect the decimal, it's there to be more precise.
As you can see, 1/4 is obviously greater than 1/8. Both fractions have 1 as a numerator, which is very helpful when it comes to comparing fractions as well as ordering them. When 1 is the numerator, the fraction is called units. It's easier to compare and order them because the smaller the denominator is, the bigger the fraction. So, 4 being a denominator is bigger than 8 being a denominator.