First, compare the digits in the thousands place of each number.
The numbers all have a 4 in the thousands place, so compare the digits in the hundreds place of each number.

Since 1 < 6, 4,186 and 4,168 are less than 4,618 and 4,681.

Next, compare the digits in the tens places of 4,186 and 4,168.

Since 6 < 8, 4,168 < 4,186.

Then, compare the digits in the tens places of 4,618 and 4,681.

Since 1 < 8, 4,618 < 4,681.

So, the numbers in order from least to greatest are
4,168, 4,186, 4,618, 4,681, and the numbers in order from greatest to least are 4,681, 4,618, 4,186, 4,168.