Final answer:
Khrushchev attacked Budapest in 1956 to suppress the Hungarian Revolution, maintain Soviet control over Eastern Europe, and prevent Hungary's exit from the Warsaw Pact.
Step-by-step explanation:
Nikita Khrushchev's decision to attack Budapest in 1956 was primarily in response to the Hungarian Revolution of that year, a national uprising where Hungarians sought an end to Soviet control and the establishment of a democratic government. Fearing the spread of anti-Soviet dissent and seeking to maintain the Warsaw Pact's influence in Eastern Europe, Khrushchev ordered the crushing of the uprising by sending troops and tanks to Hungary. The immediate triggers were Hungary's withdrawal from the Warsaw Pact and the declaration of neutrality by its leader Imre Nagy, along with appeals for Western support, which directly threatened Moscow's grip on the region.
The violent suppression of the Hungarian uprising resulted in thousands of casualties and extensive political repression, including the execution of Imre Nagy. It signaled a clear message to other Eastern Bloc countries about the consequences of defying Soviet authority and reinforced the idea that despite nominal reforms, the Soviet Union would not tolerate independence movements within its sphere of influence.