What is 8664 rounded to the nearest thousand?

Rounded to the nearest thousand means we can ignore the values in the ones & tens place (the x's are placeholders):

86xx

Now we can either round up to 9000, or down to 8000 (since we're rounding to the nearest thousand), and since the value in the hundreds place is greater than 5, this means we round up:

Answer is: 9000