The most appropriate option to fill in the blank and make a grammatically correct sentence is:
☀ than
The sentence would read: "I was determined not to stay in hospital for any longer than was strictly necessary."
Explanation: "Than" is used in comparisons to indicate a limit or extent. In this context, it's used to compare the length of stay in the hospital with what is strictly necessary. The other options don't fit the context:
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When: This doesn't convey a comparison of duration.
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Then: This doesn't convey a comparison of duration.
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That: This doesn't convey a comparison of duration.
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