So if the first sentence is gone I'd intuitively get that it'd be $11x=17(mod24)$, but I think the first sentence regarding that it's an exact multiple of 1 hour that is less than 1 day is relevant to this.

  • $\begingroup$ The first sentence just says that $x$ is an integer and $0\leq x\lt 24$ $\endgroup$ – JMoravitz Oct 17 at 19:34
  • $\begingroup$ Unless the orbital period is an integral number of hours, you can't conclude $11x\equiv17\pmod{24}$. This congruence can only be solved up to a multiple of $24$, so if we don't know that the period is less than a day, we can't what it is exactly. $\endgroup$ – saulspatz Oct 17 at 19:36

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