They're both fine, and they mean the same thing. The particle down can appear before or after the object the volume:
1a. I don't know how to turn the volume down.
1b. I don't know how to turn down the volume.
However, if the object is an unstressed personal pronoun, down has to come at the end:
2a. I don't know how to turn it down.
2b. *I don't know how to turn down it.
I marked example 2b with an asterisk *
to indicate that it's ungrammatical.
By the way, if the object is very long or complicated, down usually appears beforehand, because it would be confusing to keep the listener waiting to hear the rest of turn down:
3a. ?I don't know how to turn the volume on the stereo receiver attached to the TV over there down.
3b. I don't know how to turn down the volume on the stereo receiver attached to the TV over there.
I marked 3a with a question mark ?
to show that, although it's grammatical, it's not a very good sentence. With such a long object, it's better to put down beforehand.