Question 159822
How many single digits are there?
How many lower case letters are there?

Now, armed with that information, 
How many different digits could be in the first slot?
How many in the second one?
How many in the third?
You need to use letters in the 4th. How many letters can that be?
How many in the 5th slot?
How many different letters in the 6th?

Once you have those 6 numbers, you can find the total of different plates by multiplying as follows
{{{10 * 10 * 10 * 26 * 26 *26 }}}

See this video for a better explanation: http://collabvsl.wetpaint.com/page/Basic+Probability