Basically means the period of the function is 4π.

Time between successive high tides would be represented as the gap/distance between consecutive peaks of the function

In a typical function y = cos t, the period is 2π.

Since it is a t/k inside, now, and t/k = 1/k (t), the frequency is now 1/k of usual, which means the period is k times of the usual.

So, k (2π) = 4π
k = 2

So for this question, h = a cos (t/2) + c

At high tide, h = 21 , the maximum. This is the crest/peak of the cosine wave, so cos (t/2) = 1, its maximum value.

21 = a (1) + c
21 = a + c ①

At high tide, h = 13 , the minimum. This is the trough/valley of the cosine wave, so cos (t/2) = -1, its minimum value.

13 = a(-1) + c
13 = c - a ②

① + ② :

21 + 13 = a + c + c - a
34 = 2c
c = 17

Sub c = 17 into ②,
13 = 17 - a
a = 17 - 13 = 4

So , h = 4 cos(t/2) + 17