Let us look at each of the answer options -
A - "given in the same
year as
his appointment as chairman of Joint Chiefs of staff" - this phrase equates year to his appointment. Not a logical comparison.
B - repeats the same error that option A has.
C - correct answer. this makes perfect sense.
"that he was appointed chairman ..." modifies "year".
D - "Colin Powell gave a dedication in the same year as his appointment as chairman of the Joint Chiefs of Staff that commemorated"
The "that" is too far removed from the noun it should modify - dedication.
It seems to modify 'year/appointment'. Note that it cannot refer to 'Joint Chiefs of Staff' as we need a 'who' (to refer to people).
This also has the same error that option A has. 'year' is compared to 'his appointment'.
E - the 'that' is too far removed from the noun it must modify - dedication.
this answer option also does not make it clear who was appointed Chairman of the Joint Chiefs of Staff.
this option also equates 'year of appointment' to 'chairman of joint chiefs of staff'.
Hope this helps