Is w +6 _< w- 6 sometimes true always true or never true

It would be never true. You can tell by just plugging three random numbers in a checking.

For the first number how about we do -6.
-6+6_<-6-6= 0_<-12 which is not true

For the second number we will use 0.
0+6_<0-6= 6_<-6 which is also false

Finally we will use 6.
6+6_<6-6= 12_<0 which is also false.

I hope this helps, if you have any question just ask!!