Carlos pays a monthly fee of #$6#. In a mathematical function, this would be represented by a constant of #6#.

He also pays #8# cents, or #$0.08#, per minute spoken. If #x# were the number of minutes spoken, this would be represented by #0.08 x#.

Overall, Carlos' long distance bill can be represented by the function:

#f(x) = 0.08 x + 6#; where #f(x)# is the long distance bill, and #x# is the number of minutes spoken.

Last month, his long distance bill was #$18.64#.

Let's replace #f(x)# with #18.64#:

#Rightarrow 18.64 = 0.08 x + 6#

If we solve for #x#, we will find the number of minutes for which Carlos was billed:

#Rightarrow 12.64 = 0.08 x#

#Rightarrow 158 = x#

#therefore x = 158#

Therefore, Carlos was billed for #158# minutes.