B. To carry out only those federal laws relating to the military.
C. To carry out and law supported by the party.
D. To carry out all federal, state, and local laws.
The objective case personal pronoun is option C (him).
For example, in "I bought HIM a cigarette ("him" is an Indirect Object and also a personal pronoun).
The possessive case personal pronoun is option B (my).
For example, in "MY mother is a beautiful woman" ("my" is a possessive and also a personal pronoun).