Correct Options are:
Option A: (Negative one-fourth) cubed
Option B: Negative (one-fourth) cubed
Option D: Negative (StartFraction 1 Over 8 EndFraction) squared
Option F: Negative (one-half) Superscript 6
Step-by-step explanation:
We need to check the expressions that have value 
Option A: (Negative one-fourth) cubed

Solving: 
We get 
So, Option A is correct.
Option B: Negative (one-fourth) cubed

Solving: 
We get 
So, Option B is correct
Option C: (Negative StartFraction 1 Over 8 EndFraction cubed

Solving: 
We get 
So, Option C is not correct.
Option D: Negative (StartFraction 1 Over 8 EndFraction) squared

Solving: 
We get 
So, Option D is correct.
Option E: (Negative one-half) Superscript 6

Solving:
We get: 
So, Option E is not correct.
Option F: Negative (one-half) Superscript 6

Solving:
We get: 
So, Option F is correct.
So, correct Options are: Option A, B, D and F