Given information:
- The nth term of the arithmetic progression (AP) is defined as tn.
- The sum of the first 'n' terms of the AP is defined as Sn.
- |t8| = |t16|, which means the absolute values of the 8th and 16th terms are equal.
- t3 is not equal to t7, which means the 3rd and 7th terms are not equal.

To find: The value of S23, the sum of the first 23 terms of the AP.

Solution:
1. Finding the common difference:
Since tn represents the nth term of the AP, we can write tn = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.
2. Using the given information, we can form two equations:
t8 = a + 7d
t16 = a + 15d
3. Since |t8| = |t16|, we can write:
|a + 7d| = |a + 15d|
4. Expanding the absolute values, we get two cases:
a + 7d = a + 15d or a + 7d = -a - 15d
8d = 8a or 14d = -2a
4d = 4a or 7d = -a
5. Simplifying the equations, we find:
d = a or 7d = -a
6. If d = a, then the AP is constant, which means all the terms are the same. However, this contradicts the given information that t3 is not equal to t7. Therefore, d cannot be equal to a.
7. If 7d = -a, then we can substitute this into the equation tn = a + (n-1)d to find tn in terms of n:
tn = -7d + (n-1)d
tn = -7d + nd - d
tn = -6d + nd
8. Now, we can find the sum of the first 23 terms, S23:
S23 = t1 + t2 + t3 + ... + t23
S23 = (-6d + d) + (-6d + 2d) + (-6d + 3d) + ... + (-6d + 23d)
S23 = -6d(1 + 2 + 3 + ... + 23) + (1 + 2 + 3 + ... + 23)d
S23 = -6d(23(23+1)/2) + (23(23+1)/2)d
S23 = -6d(276) + (276)d
S23 = -1656d + 276d
S23 = -1380d
9. Since d is not equal to zero (as d = a is not possible), we can conclude that S23 = 0.

Therefore, the correct answer is option 'D', 0.