Option 1: zestfully -> means with enthusiasm and energy, which doesn't match the contemplative, nostalgic mood of remembering the past.
Option 2: yieldingly -> means submissively or compliantly, which doesn't logically fit with the act of gazing at something.
Option 3: yearningly -> means with deep longing or desire, perfectly capturing the nostalgic emotion of looking at one's childhood home while reminiscing.
Option 4: woefully -> means sadly or miserably, too negative given the context mentions "beautiful" home and "memorable" (not tragic) past.
Hence, Option 3: yearningly -> This word best conveys the sense of nostalgic longing and wistful emotion someone feels when gazing at their childhood home and thinking about cherished memories from the past -> correct