Is this along the lines of what you're looking for? If not, post some more information. The query below joins up the sales, sales line, beverage, recipe, and products tables, and then calculates the quantity sold based on the quantity of beverages sold and the amount in the recipe. I didn't test this. You can add a WHERE clause to restrict based on date, product, etc, as desired.
QUANTITY SOLD:
SELECT pr.prod_id
, pr.prod_name
, SUM(sl.qty*rc.qty) AS qty_sold
FROM sales sa JOIN sales_line sl ON sa.sales_id = sl.sales_line_id
JOIN beverage bv ON sl.bev_id = bv.bev_id
JOIN recipe rc ON bv.bev_id = rc.bev_id
JOIN products pr ON rc.prod_id = pr.prod_id
WHERE ...
GROUP BY pr.prod_id
, pr.prod_name
QUANTITY PURCHASED:
SELECT pr.prod_id
, pr.prod_name
, SUM(pl.qty) AS qty_purch
FROM purchase pc JOIN purchase_line pl ON pc.purch_id = pl.purch_id
JOIN products pr ON pl.prod_id = pr.prod_id
WHERE ...
GROUP BY pr.prod_id
, pr.prod_name