Maybe this will help with the thinking process:
If one compared a meter to a ten dollar bill (Think ONE THOUSAND PENNIES)
One meter (39.37 inches) = 1000 pennies
One centimeter = 10 pennies (1/100 of the meter - think perCENT or CENTS in a dollar)
One millimeter = 1 penny (1/1000 of a meter - or 1/10 of a centimeter)
The simpler way of doing it is to just get a ruler, measuring stick, or tape measure with both units on it and measure using the guide.
The approximate equivalents are:
One meter - one yard plus 3-1/2 inches
One centimeter - a couple of threads more than 3/8 of an inch
6 millimeters - about 1/4 inch
2/3 of a centimeter - about 1/4 inch