The correct answer to this open question is the following.
The “crack problem” Gorbachev faced in the late 1980s was the dissolution of the Soviet Union.
The cartoon shows Soviet leader Mikhail Gorbachev with a glue tube in his hands. He is in shock because in front of him is the map of the USSR territory cracking. He faced this problem because of the disintegration of the republics that formed the Soviet Union, a problem that became notorious in the mid-1980s. The Soviet Union ceased to exist on December 26, 1991. Gorbachev had resigned one day before and the new leader of Russia was Boris Yeltsin.