a=7 correct (half the distance between high and low tide)
The average time difference between high tides is the period of the function. So \(\displaystyle \frac{2\pi}{b} = 12.4\). So b=??
The value of d depends on how you define H.
If you let H= "height above low tide" then d=7. In this case H=0 at low tide.
If you let H = "height above "mid-tide" " then d=0. Here H=-7 at low tide.
Also. the value of c depends on where you are measuring time from.
If you measure time from mid-tide on a rising tide c=0.
If you measure time from high tide then c = \(\displaystyle \frac{1}{4}*12.4 = 3.1\)
Personally I would choose the bold options above. The equation would be: H = ???
The graph would have the equilibrium line at y=7 (ie d). It would begin at the maximum point (0, 14), cut the equilibrium line at(3.1, 7) have a minimum on the x-axis at (6.2, 0) up to the equilibrium line again at (9.3, 7) up to a max again at (12.4, 14).
Other answers would be possible depending on how H and t are defined ie where they are measured from.