You would need three wildcard certificates:
*. east.company.com
*. central.company.com
*. west.company.com
The common domain in each of the domains is company.com. However, a wildcard covers only one level of subdomain. For example: *. company.com will cover "<anything>.company.com" but it won't cover "<anything>.<anything>.company.com".
You can only have one wildcard in a domain. For example: *.company.com. You cannot have *.*.company.com. Only the leftmost wildcard (*) is counted.
Incorrect Answers:
A: You cannot secure public facing server farms without any SSL certificates.
B: You need three wildcard certificates, not one. A wildcard covers only one level of subdomain.
D: You do not need six wildcard certificates to secure three domains.
References:
https://uk.godaddy.com/help/what-is-a-wildcard-ssl-certificate-567