Answer:
C) SN2 and E2
Step-by-step explanation:
For this question, we have analyzed the substrate and the base/nucleophile. The substrate, in this case, is 1-iodohexane and the base/nucleophile is potassium tert-butoxide.
Substrate
In the 1-iodohexane the iodide "I" is bonded to a primary carbon (carbon 1). Therefore we will have a primary substrate. If we have a primary substrate an Sn1 can not take place. We can not have a primary carbocation due to this instability. So, we can disccard options A) and B).
Base/nucleophile
In the potassium tert-butoxide we have an ionic compound. A positive charge is placed in the potassium atom a negative charge is placed in the oxygen of the ter-butoxide ion. So, we will have a strong base (a molecule with the ability to remove electrons) and a strong nucleophile (a molecule with ability to bond with an electrophile). With all this in mind, we can not have an E1 reaction.
With both analyses, the answer is C).
See figure 1
I hope it helps!