There are 6 ways to choose the first digit.

For each of those 6 ways to chose the first digit,
There are 5 ways to choose the second digit.
That's 6∙5=30 ways to choose the first two digits.

For each of those 6∙5=30 ways to chose the first two digits,
There are 4 ways to choose the third digit.
That's 6∙5∙4 = 120 ways to choose the first three digits.

For each of those 6∙5∙4 = 120 ways to chose the first three digits,
There are 5 ways to choose the fourth digit.
That's 6∙5∙4∙3 = 360 ways to choose the first four digits.

For each of those 6∙5∙4∙3 = 360 ways to chose the first four digits,
There are 2 ways to choose the fifth digit
That's 6∙5∙4∙3∙2 = 720 ways to choose the first five digits.

And since that's all the digits, the answer is 6∙5∙4∙3∙2 = 720.

Edwin