A student exhibiting a challenge with auditory figure-ground would struggle to:

A student dealing with auditory figure-ground issues indeed struggles primarily with filtering out background noise to focus on a specific sound or voice amidst competing sounds. This difficulty manifests as an inability to discern a particular auditory signal against a noisy backdrop, such as focusing on the teacher's voice while other students are talking.

In situations like a classroom setting, this challenge becomes apparent when the student finds it hard to pay attention to what the teacher is saying due to the distractions created by their peers. This scenario demonstrates the core of auditory figure-ground processing, where the student effectively cannot differentiate the foreground sound (the teacher) from the background noise (classmates chatting).

While the other options might relate to auditory processing to some extent, they do not directly encapsulate the essence of auditory figure-ground challenges. Distinguishing letters, writing notes, and memorizing song lyrics involve various forms of visual and cognitive processing, not primarily the discrimination of auditory signals in a noisy environment. Thus, the correct answer specifically highlights the difficulties associated with auditory figure-ground processing.