The pair of verb forms which correctly completes the sentence is the following one:
A. are; appears.
The complete sentence would look like this:
"Mercury and Venus are relatively close to the sun, and neither Mercury nor Venus appears to support life."
In the first clause, the subject is formed by "Mercury and Venus", which means it is plural, and therefore it requires a plural verb (<em>Mercury and Venus</em> are= <em>They</em> are).
In the second clause, there is a neither...nor construction, and both elements which form the subject (again, <em>Mercury and Venus</em>, but this time used in the construction <u>neither</u><u><em> Mercury </em></u><u>nor</u><u><em> Venus</em></u>) are singular nouns, which means a singular verb must be used: neither Mercury nor Venus <em>appears</em>.
