Final answer:
A child will not differentiate the minimal pair 'Cage' and 'gauge' if he is demonstrating assimilation phonological process.
Step-by-step explanation:
The phonological process demonstrated by a child's inability to differentiate between the minimal pair 'cage' and 'gauge' is:
1) Assimilation.
Assimilation in phonology refers to the process where a sound in a word becomes more similar or identical to another sound in the same word or a nearby word due to the influence of neighboring sounds. In this case, the child might assimilate the sounds /k/ and /g/ because they share certain characteristics like voicing or place of articulation, causing difficulty in distinguishing between the words 'cage' and 'gauge.' This phonological process of assimilation can result in the interchangeability or lack of differentiation between similar sounds in words, affecting the child's perception or production of those sounds.