LLC (Logical Link Control) and VC-Mux (Virtual Circuit Multiplexing) are two different methods of data framing or "encapsulation" that are commonly used when transmitting data via a DSL connection.
They are methods of supporting multiple layer 3 protocols (eg IP, Novell IPX or Appletalk) over a single physical circuit, using 1 or more Virtual Circuits, such as the ATM circuit you are using for DSL.
LLC/SNAP embeds a protocol type field into the headers of the layer 2 frame used (the SNAP header), which describes what layer 3 protocol type is being carried within the frame. The device (a router) at the other end looks at this field, and then determines that IP packets should go to the IP forwarding software, IPX packets should go to the IPX forwarding software etc. LLC/SNAP works over a single Virtual Circuit.
VC-Mux on the other hand, uses a separate Virtual Circuit for each different layer 3 protocol.
LLC/SNAP is more efficient when each VC costs money - you only use one for all the Layer 3 protocols your network is using.
VC-Mux is more efficient for transmitting data, as you don't need the protocol type field (and other) overheads.
I'm not exactly sure which type aus DSL uses, VC-Mux would be preferable, as the Internet only runs on layer 3 protocol, that being IP :-)
For more of the details (and probably a better explanation than mine), have a look at rfc2684, formerly rfc1483.
www.faqs.org/rfcs/rfc2684.html