Scotty said that he can have Spock back in Vulcan in 4 days...

Slingshot around the sun or tapdance on the deflector dish. Who cares?

Warp Drive, in the Star Trek universe, is a faster a than light drive.

That implies a speed of about four light years a day, or about 1,461 times the speed of light. To be precise, if Vulcan is 16.0 to 17.0 light years from Earth, and it would take 3.0 to 5.0 Earth days to reach Vulcan, the speed would be between 1,168.8 and 2,069.25 times the speed of light.

According to the alleged TOS warp speed formula, the speed of a warp factor would equal the speed of light times the warp factor number cubed.

Warp factor 1 would be 1 times the speed of light.

Warp factor 2 would be 8 times the speed of light.

Warp factor 3 would be 24 times the speed of light.

Warp factor 4 would be 64 times the speed of light.

Warp factor 5 would be 125 times the speed of light.

Warp factor 6 would be 216 times the speed of light.

Warp factor 7 would be 343 times the speed of light.

Warp factor 8 would be 512 times the speed of light.

Warp factor 9 would be 729 times the speed of light.

Warp factor 10 would be 1,000 times the speed of light.

Warp factor 11 would be 1,331 times the speed of light.

Warp factor 12 would be 1,728 times the speed of light.

Warp factor 13 would be 2,197 times the speed of light.

And so on.

So a voyage to Vulcan could be made in 3 to 5 days using a warp factor somewhere between warp 10 and warp 13. I believe it was said the new engines in Star Trek: The Motion Picture could reach warp factor 12, although I don't know whether that was said in the movie and thus is canonical.

And of course the TOS warp scale was never specified in any canon production.

Of course, nobody said that Vulcan was 16 light years from Earth in Star Trek: The Motion Picture. When Star Trek: The Motion Picture was made Vulcan might have been considered to be much farther from Earth, or possibly much closer to Earth, than 16 light years.

I note that in the TOS episode "Metamorphosis" Zefram Cochrane, inventor of warp drive, knew what Vulcans looked like. Naturally the first Earth ships with warp drive werre probably much slower than TOS ships. Thus that would indicate that Vulcan was relatively close to Earth.

Says who?