The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
2. Replace Left Join With Subquery (modified query below): The pattern of inflating the amount of data (using joins) and deflating (using GROUP BY) usually slows down queries. In this case, it can be avoided by moving some of the logic to the SELECT clause, and therefore removing some of the LEFT JOINs. In some cases, this transformation can lead to an obsolete GROUP BY clause, which can also be removed.

Optimal indexes for this query:

ALTER TABLE `tableCars` ADD INDEX `tablecars_idx_manid_val` (`Manid`,`val`);
ALTER TABLE `tableManufactures` ADD INDEX `tablemanufactures_idx_val` (`val`);
ALTER TABLE `tableTrucks` ADD INDEX `tabletrucks_idx_manid_val` (`Manid`,`val`);
ALTER TABLE `tableVans` ADD INDEX `tablevans_idx_manid_val` (`Manid`,`val`);

The optimized query:

SELECT
        tM.val,
        (SELECT
            min(t1.val) AS MakesCars 
        FROM
            tableCars t1 
        WHERE
            tM.id = t1.Manid LIMIT 1) AS MakesCars,
        (SELECT
            min(t2.val) AS MakesTrucks 
        FROM
            tableTrucks t2 
        WHERE
            tM.id = t2.Manid LIMIT 1) AS MakesTrucks,
        (SELECT
            min(t3.val) AS MakesVans 
        FROM
            tableVans t3 
        WHERE
            tM.id = t3.Manid LIMIT 1) AS MakesVans 
    FROM
        tableManufactures tM 
    ORDER BY
        tM.val