I have 3 tables:
|**Product ID**|**Product Description**|
|--------------|-----------------------|
|1 |Wine |
|2 |Ruler |
|3 |Gas |
|4 |Water |
|**Group ID**|**Group Description**|
|------------|---------------------|
|1 |Cheetahs |
|2 |Elephants |
|3 |Cougars |
|**GroupID**|**Product ID**|**Amount Sold**|**Day Sold**|
|-----------|--------------|---------------|------------|
|1 |2 | 3|07-31-2016 |
|1 |1 | 1|07-31-2016 |
|2 |3 | 5|07-31-2016 |
|1 |4 | 2|08-01-2016 |
|**Group ID**|**Product ID**|**Amount Sold**|
|------------|--------------|---------------|
|1 |1 |1 |
|1 |2 |3 |
|1 |3 |0 |
|1 |4 |0 |
|2 |1 |0 |
|2 |2 |0 |
|2 |3 |5 |
|2 |4 |0 |
|3 |1 |0 |
|3 |2 |0 |
|3 |3 |0 |
|3 |4 |0 |
SELECT
g.GroupId
,p.ProductId
,SUM(COALESCE(s.AmountSold,0)) as AmountSold
FROM
Products p
CROSS JOIN Groups g
LEFT JOIN Sales s
ON p.ProductId = s.ProductId
AND g.GroupId = s.GroupId
AND daySold = '07-31-2016'
GROUP BY
g.GroupId
,p.ProductId
ORDER BY
g.GroupId
,p.ProductId
SELECT
g.GroupId
,p.ProductId
,SUM(COALESCE(s.AmountSold,0)) as AmountSold
FROM
Products p
CROSS JOIN Groups g
LEFT JOIN Sales s
ON p.ProductId = s.ProductId
AND g.GroupId = s.GroupId
AND s.daySold = '07-31-2016'
GROUP BY
g.GroupId
,p.ProductId
ORDER BY
g.GroupId
,p.ProductId
Note your expected results you provided are wrong for group 1 product 4 there were 2 of those in the sale.