The optimization process and recommendations:

1. Avoid LIKE Searches With Leading Wildcard (query line: 43): The database will not use an index when using like searches with a leading wildcard (e.g. '%1%'). Although it's not always a satisfactory solution, please consider using prefix-match LIKE patterns (e.g. 'TERM%').
2. Avoid LIKE Searches With Leading Wildcard (query line: 29): The database will not use an index when using like searches with a leading wildcard (e.g. '%1%'). Although it's not always a satisfactory solution, please consider using prefix-match LIKE patterns (e.g. 'TERM%').
3. Avoid Subqueries (query line: 18): We advise against using subqueries as they are not optimized well by the optimizer. Therefore, it's recommended to join a newly created temporary table that holds the data, which also includes the relevant search index.
4. 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.

Optimal indexes for this query:

ALTER TABLE `estimatemaster` ADD INDEX `estimatemaster_idx_estimateid` (`estimateid`);
ALTER TABLE `simpleestimatedetails` ADD INDEX `simpleestimatedeta_idx_simpleestid` (`simpleestid`);
ALTER TABLE `vcustomer_prospect` ADD INDEX `vcustomer_prospect_idx_customerid` (`customerid`);

The optimized query:

SELECT
        Concat(e.estimate1,
        '-',
        e.estimate2) AS estimateid,
        e.estimatetype,
        e.createdby,
        e.estimateid AS estID,
        e.`layoutnumber`,
        sd.specno,
        sd.samplenumber,
        sd.numberon,
        c.customerid,
        c.custprosname,
        c.`custtype`,
        (SELECT
            Count(*) 
        FROM
            (SELECT
                e.estimate1 
            FROM
                `simpleestimatedetails` sd,
                estimatemaster e,
                `vcustomer_prospect` c 
            WHERE
                c.customerid IN (
                    e.customernumber, e.prospectnumber
                ) 
                AND (
                    e.estimate1 LIKE '%1%'
                ) 
                AND (
                    sd.`simpleestid` = e.estimateid
                )) AS counter) AS counter 
        FROM
            `simpleestimatedetails` sd,
            estimatemaster e,
            `vcustomer_prospect` c 
        WHERE
            c.customerid IN (
                e.customernumber, e.prospectnumber
            ) 
            AND (
                e.estimate1 LIKE '%1%'
            ) 
            AND (
                sd.`simpleestid` = e.estimateid
            )