Thanks for the question. I thought I knew the answer upon reading the question (based upon reading BOL, not personal experience), but I wasn't sure. Since the question referenced SQL 2012, I thought that ALTER SYNONYM might have been added with that version (or with SQL 2014, in which case the question would have been designed to "trip up" someone into thinking that it was available in SQL 2012), but it's not available in SQL 2014, either.
This makes me wonder what else is in SQL that has CREATE and DROP, but not ALTER functionality. :unsure: Hey, that might make an excellent multiple-choice QOTD!