How did Alexander the Great encourage the blending of eastern and western cultures?
First, Alexander helped bring together eastern and western cultures by the simple fact of his invasion. By entering the Persian Empire and parts eastward, he brought together people formerly only linked indirectly through trade routes. Of course, he did so by conquest, and Alexander's campaigns were marked by great destruction and death. But he also demonstrated a great interest in other cultures, bringing a group of scholars and philosophers alongside his army to record what they learned about the foreign cultures they encountered. He was also notably tolerant of local religions, and promoted cultural interaction by example, marrying local women and encouraging his officers to do the same. He even, much to the consternation of many of his men, adopted Persian-style ceremonies in his court in Babylon. Overall, Alexander did not begin interactions between east and west, which were already beginning to develop through the Persian Empire and the nascent Silk Road trade routes. But he did accelerate them, and Greek influence can be seen in iconography as far east as Han China, while Persian and Indian influences quickly infilitrated the Mediterranean after Alexander's brief conquests.
Alexander was an internationalist in the widest sense. Unlike his father, Alexander was curious about the foreign cultures, especially in Asia, that he came into contact with. He enjoyed enthnography and assimilated many of the cultures, such as the Persians, into his own, much to the chagrin of the Macedonians. Remember, he was tutored as a youngster by Aristotle and took Aristotle's nephew, Callisthenes, along as his biographer. In many ways, Alexander was a leader without blemish; his men would do anything for him which they proved over nearly a decade of hard marching and conquest. But it was his insistence on pushing further and further East and his fascination and appreciation of Asian cultures that led to a mutiny outside of India. He also took a foreign wife, Roxanne, much to his men's displeasure. I would recommend you read Peter Green or Robin Lane Fox's description of Alexander's program of acculturation and how he favored many key personages, such as Bagoas, more than his own men.