There are 6 ways to choose the first digit.

For each of those 6 ways to chose the first digit,
There are 6 ways to choose the second digit.
That's 6∙6=62=36 ways to choose the first two digits.

For each of those 6∙6=36 ways to chose the first two digits,
There are 6 ways to choose the third digit.
That's 6∙6∙6 = 63 = 216 ways to choose the first three digits.

For each of those 6∙6∙6 = 63 = 216 ways to chose the first three digits,
There are 6 ways to choose the fourth digit.
That's 6∙6∙6∙6 = 64 = 1296 ways to choose the first four digits.

For each of those 6∙6∙6∙6=64 = 1296 ways to chose the first four digits,
There are 6 ways to choose the fifth digit
That's 6∙6∙6∙6∙6 = 65 = 7776 ways to choose the first five digits.

And since that's all the digits, the answer is 6∙6∙6∙6∙6 = 65 = 7776.

Edwin