Q: What major event happened on June 3rd, 1989?
A: On the night of June 3–4, 1989, Chinese authorities sent troops and tanks into Beijing. The U.S. Department of State’s Office of the Historian records that the People’s Liberation Army stormed Tiananmen Square and suppressed the demonstrations. State Department: Tiananmen Square, 1989
A Senate press release summarizing a congressional resolution states that armed troops entered Beijing on the afternoon and evening of June 3, 1989, and that firing into crowds continued into the morning of June 4. Senate: Tiananmen Square resolution context
A Department of Justice chronology also lists June 3, 1989 as the date Ayatollah Ruhollah Khomeini died, citing contemporary reporting. DOJ chronology PDF
I cannot independently verify casualty totals from these pages. Official U.S. accounts treat the Tiananmen crackdown as the main event associated with that date.