Very simple to understand solution.

// Complete the birthday function below.
static int birthday(List<Integer> s, int d, int m) {
    int length = s.size();
    int numWays = 0, sum = 0;

    for(int i = 0 ; i <= (length - m) ; i++){
        for(int j = 0 ; j < m ; j++){
            sum = sum + s.get(j+i);
        }
        if(sum == d){
            numWays++;
        }
        sum = 0;
    }
    return numWays;
}