The Core Idea

If $prefix[j] - prefix[i] = k$, then the subarray from $i+1$ to $j$ has sum $k$. Rearranging: $prefix[i] = prefix[j] - k$.

For each $j$, count how many $i < j$ have $prefix[i] = prefix[j] - k$. That's how many subarrays ending at $j$ have sum $k$.

Use a hash map to count occurrences of each prefix sum. For each new prefix sum, look up how many times $(current - k)$ has appeared.