EDIT: Info, since someone asked an their comment was removed
Here’s the Wikipedia page for the explorer. They don’t know what sea it is, but most guess the Red Sea, Black Sea, or Mediterranean.
According to a document (compiled a few later?), the ambassador was told:
“The ocean is huge. Those making the round trip can do it in three months if the winds are favourable. However, if you encounter winds that delay you, it can take two years. That is why all the men who go by sea take stores for three years. The vast ocean urges men to think of their country, and get homesick, and some of them die.”
So take that with a grain of salt since it isn’t contemporary, but there’s clearly some sort of expectation that they would be able to communicate linguistically, not just through gestures.
Gan Ying probably had an interpreter who knew Greek and/or Aramaic.
The quote in your question comes from the History of the Later Han (Hou Hanshu), compiled by the historian Fan Ye in the fifth century CE. A translation and very helpful commentary are available online here.
Gan Ying seems to have reached the head of the Persian Gulf, and probably stopped at the Parthian city of Charax in what is now southern Iraq. Ethnically, the population of this city and marshy region around it was largely Arab (or so Pliny the Elder claims (NH 6.30)). To judge from the city's coins and inscriptions, however, at least the ruling classes of first-century Charax knew Aramaic and Greek.
Both languages were widely known from Mesopotamia to central Asia.
Although Aramaic was chiefly spoken in Syria, Palestine, and Mesopotamia, it was employed as a language of trade and diplomacy far beyond these regions. Aramaic had been used as an official language by the Achaemenid Persians throughout their vast empire, including in central Asia. In Bactria (now parts of Afghanistan and Tajikstan), Aramaic became an important language of commerce, as attested by a recently-published cache of documents from the fourth century BCE.
After Alexander's conquest of the Persian Empire, Greek replaced Aramaic as the language of government. Bactria became a particularly important eastern outpost of Hellenism; and even after the Greek kingdom of Bactria was wiped out by nomads, Greek continued to be spoken in the region for centuries- probably at least until the time of Gan Ying's expedition.
Gan Ying traveled at the time when the frontiers of the Han Dynasty extended deep into the central Asia. His route through Parthia (traced here) probably began in the Tarim Basin. He would have entered Parthian territory somewhere in Bactria - the same region where Greek and (probably) Aramaic were still spoken. There would have been a few "Silk Road" merchants in Merv and other Bactrian cities who knew (a little) Chinese and one or both of these languages; Gan Ying must have convinced one or more of these men to accompany him as an interpreter.