You could get the count for each distinct fruit value in the Fruit1 and Fruit2 columns, and then add those together with a SUM aggregate.
The "trick" is to use an inline view that concatenates the two results together with a UNION ALL set operator.
SELECT f.fruit, SUM(f.cnt) AS cnt
FROM ( SELECT d.Fruit1 AS fruit, COUNT(1) AS cnt FROM Fruits d GROUP BY d.Fruit1
UNION ALL
SELECT e.Fruit2 AS fruit, COUNT(1) AS cnt FROM Fruits e GROUP BY e.Fruit2
) f
GROUP BY f.fruit
ORDER BY f.fruit