Analysis:
Clause 1: One (One of the acts- Singular) of Ronald Reagan's first acts as President was (Singular verb) to rescind President Carter's directive

Clause 2: that (refers to directive - Subject of the Clause 2) any chemical banned on medical grounds in the United States be (Singular Verb) prohibited from sale to other countries (Idiom Prohibited x from Y).
Directive - Base form of the verb "be"

Choices

(A) that any chemical banned on medical grounds in the United States be prohibited from
sale to other countries (Idiom Issue Prohibited X from Y)
(B) that any chemical be prohibited from sale to other countries that was banned on
medical grounds in the United States (Countries that was banned- countries were not banned it is the chemical that was banned)
(C) prohibiting the sale to other countries of any chemical banned on medical grounds in the
United States .....Seems Okay (prohibiting X=the sale to Y other countries)
(D) prohibiting that any chemical banned on medical grounds in the United States is sold to
other countries (Idiom issue)
(E) that any chemical banned in the United States on medical grounds is prohibited from
being sold to other countries. (Idiom issue + being)