I am having trouble figuring out some segments and how they apply to numbers of letters. I am understanding words having more letters than segments, but not more segments than letters. For example, is there a word with 3 letters and 4 segments?
What is your definition of segment?
an individual speech sound. i have been trying some out and think i may have figured it out. for example:

at has two segmets - ae t
math has three segments - m ae Emotion: movie (theta)

would spy be an example of a word with four segmets, since phonetically it is s p a i?
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I belive there might be, thou i dont know.

The word "pharynx" has seven letters and seven segments.

Segment 1: ph, 2: a, 3: r, 4: y, 5: n, 6+7: x (sound of k and s)