How did franklin d. roosevelt's multiple terms in office affect passage of the twenty-second amendment?

The answer is: It limited the President to two consecutive terms

At that time, Roosevelt tried to made himself elected for the fifth term, leveraging from his popularity acquired from the new deal. His action caused direct opposition from both parties, which lead to a change in the twenty second amendment.

The twenty-second amendment  now specify that the president could only serve at the office for the maximum of 8 years and two consecutive terms.