Received a PM asking me to respond.

The new telescope uses lens that show six times as far as a refractor telescope does
The new telescope uses lens that show six times further than a refractor telescope does
The new telescope uses lens that show six times farther than a refractor telescope does
The new telescope uses lens that show six times as farther as a refractor telescope does

All four sentences are incorrect as written above. You can't "show" farther than something else can "show."

You could say:
The new telescope allows one to see six times farther than one can using a refractor telescope." (There are other ways to convey this same information; this is just one example of a correct sentence.)

The meaning of the above:
If the refractor telescope allows you to see for x feet, then the new telescope allows you to see for x + 6x = 7x feet.

You could also say:
The new telescope allows one to see six times as far as one can using a refractor telescope."

This one means:
If the refractor telescope allows you to see for x feet, then the new telescope allows you to see for 6x feet.

This language difference is most important in a quant question, because it changes the number you need to use.

Offiically, when talking about a distance, the correct word is "farther," not "further" (though lots of people use the two words interchangeably today).

Finally, it is never correct to say "as farther as." It's either "as far as" or "farther than."