Chapter 23 - How many shuttles did the Enterprise carry? (Patreon)

The answer is from the technical manual and as the Tikuma is a galaxy-class herself, I think the answer is same for that ship too.

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The standard complement for this class of ship included ten standard personnel shuttles, ten cargo shuttles, and five special purpose craft. The Tikuma also carried twelve two-person shuttlepods for extravehicular and short-range use.

Operating rules required that at least eleven shuttle vehicles be maintained at operational status at all times. Cruise Mode operating rules required one standard shuttlecraft and one shuttlepod to be at urgent standby at all times, available for launch at five minutes' notice. Four additional shuttlecraft are always available on immediate standby (thirty minutes to launch), and an additional six vehicles are maintained for launch with twelve hours' notice. Red Alert Mode operating rules require two additional shuttles to be brought to urgent standby, and all nine remaining operational vehicles to be maintained at immediate standby.