The correct answer is option B: 3-methylpent-2-ene.

Explanation:
- The E-Z mechanism is a notation system used to describe the stereochemistry of double bonds in organic molecules.
- It is based on the priority of groups attached to the double bond, where higher priority groups are given priority in the E-Z notation.
- In order to determine the E-Z configuration of a double bond, we need to assign priorities to the atoms or groups attached to the double bond.
- The priority is determined based on the atomic number of the atoms directly attached to the carbon atoms of the double bond.
- If the two highest priority groups are on the same side of the double bond, it is termed as Z (from the German word zusammen, meaning together).
- If the two highest priority groups are on opposite sides of the double bond, it is termed as E (from the German word entgegen, meaning opposite).
- Now let's analyze the given options:
- Option A: 2-methylpent-2-ene does not have a double bond.
- Option B: 3-methylpent-2-ene has a double bond between the second and third carbon atoms. The two highest priority groups, the methyl group and the ethyl group, are on opposite sides of the double bond, satisfying the E-Z notation. Therefore, this option shows the E-Z mechanism.
- Option C: Methyl-3-pent-2-ene does not have a double bond.
- Option D: 2,3-methylpentene does not have a double bond.
- Hence, the correct answer is option B: 3-methylpent-2-ene, as it shows the E-Z mechanism.