shell# echo "you are $(( $(date +%Y)-bday )) years old"
So, by putting the entire calculation inside $(( )) makes it interpreted as a numerical (mathematical) operation.
Inside the $(( )) I have subtracted the variable $bday from the output of $(date +%y).
You pretty much have it correct in your last post; however, your echo statement is actually echoing the "=" sign, because it is simply part of the string you are echoing. It has no mathematical significance in the string.