We know that a larger quantity has lesser number of objects than the smaller quantity.
For example we know if a distance is 1 km, it shall have 1000 units of meter.
so in 5 km which is 5 times 1 km, there shall be 5 times 1000 units of meter.
That is why when converting from larger to smaller units we multiply.
Now we know centimeter is a larger unit & millimeters is a smaller unit.
So when we need to convert to millimeters from centimeters we need to multiply.