Just like a pair and a dozen, a mole is a word that means "this many" or a certain amount.

How many does a pair stand for?

1.   ?    2
2.   ?    4
3.   ?    5
4.   ?    10
5.   ?    12

If I have a pair of socks, I have 2 socks.

How many is a dozen?

1.   ?    2
2.   ?    4
3.   ?    5
4.   ?    10
5.   ?    12

Both a "pair"and a dozen are words that mean "this many".

How many things is one mole?

1.   ?    10
2.   ?    100
3.   ?    1,000,000
4.   ?    6.02 x 10²³

Yes. A mole of anything means you have 6.02 x 10²³ of that thing.

How many socks do I have if I have 1 mole of socks?

1.   ?    12
2.   ?     6.02 x 10²³
3.   ?    2
4.   ?     12.04 x 10²³

How many atoms do I have if I have a mole of Beryllium atoms?

1.   ?     6.02 x 10²³
2.   ?    12
3.   ?    12.04 x 10²³
4.   ?    9.012

How many atoms do I have if I have a mole of Carbon atoms?

1.   ?     6.02 x 10²³
2.   ?    12
3.   ?    12.04 x 10²³
4.   ?    9.012

So every mole of something is 6.02 x 10²³.

How many atoms do I have if I have 2 moles of Carbon atoms?

1.   ?     6.02 x 10²³
2.   ?    3 x (6.02 x 10²³) = 18.06 x 10²³
3.   ?     2 x (6.02 x 10²³) = 12.04 x 10²³
4.   ?    9.012 g

How many molecules in 3 moles water?

1.   ?    2 x (6.02 x 10²³) = 12.04 x 10²³
2.   ?    6.02 x 10²³
3.   ?    3 x (6.02 x 10²³ ) = 18.06 x ²³
4.   ?    18.02 grams

To find out how many atoms or molecules you have, multiply the number of moles by 6.02 x 10²³.
Now let's try to go the other way.

If I have 6.02 x 10²³ atoms of Fluorine, how many moles do I have?

1.   ?    1
2.   ?    2
3.   ?    3
4.   ?    4
5.   ?    6.02 x 10²³

How many moles are there in 6.02 x 10²³ molecules of carbon dioxide?

1.   ?    1
2.   ?    2
3.   ?    3
4.   ?    4
5.   ?    6.02 x 10²³

How many moles are there in 12.04 x 10²³ molecules of diatomic oxygen (O₂)?

1.   ?    1
2.   ?    2
3.   ?    3
4.   ?    4

In order to go from the number of atoms or molecules (or even socks!) to the number of moles, you divide by 6.02 x 10²³.

How many moles are there in 18.06 x 10²³ atoms of iron?

1.   ?    1
2.   ?    2
3.   ?    3
4.   ?    4

In order to go from number of moles to number of atoms or molecules:

1.   ?    multiply by 6.02 x 10²³.
2.   ?    divide by 6.02 x 10²³.

To go from number of atoms or molecules to number of moles:

1.   ?    multiply by 6.02 x 10²³.
2.   ?    divide by 6.02 x 10²³.