Final answer:
Infants can typically discern between the phonetic sounds [ba] and [ga] at around 6 months of age, as they develop the ability to engage with two-syllable sounds and exhibit improvement in cognitive and motor skills.
Step-by-step explanation:
Infants have the ability to discern between different phonetic sounds from an early age. By 6 months, infants typically engage in vocal play and may already be starting to produce two-syllable sounds such as "mama" and "dada", which suggests they are developing the ability to distinguish between different speech sounds. Additionally, they show advances in multiple areas of cognition and motor skills, such as sitting or pulling themselves into a sitting position, as well as showing improved visual acuity and color perception.
Studies in language development also indicate that infants are initially capable of discriminating between the phonemes of all human languages, but by 12 months, this ability becomes more specialized to the phonemes they are exposed to in their environment. Hence, the answer to the question of at what age infants can hear the difference between [ba] and [ga] would be at approximately 6 months of age.