The optimization process and recommendations:

1. Avoid LIKE Searches With Leading Wildcard (query line: 10): The database will not use an index when using like searches with a leading wildcard (e.g. '%8%'). Although it's not always a satisfactory solution, please consider using prefix-match LIKE patterns (e.g. 'TERM%').
2. Avoid Selecting Unnecessary Columns (query line: 2): Avoid selecting all columns with the '*' wildcard, unless you intend to use them all. Selecting redundant columns may result in unnecessary performance degradation.
3. 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 `catch_estimation` ADD INDEX `catch_estimation_idx_month_centername` (`month`,`centername`);
ALTER TABLE `gearwise_estimation` ADD INDEX `gearwise_estimatio_idx_estimationid` (`estimationid`);

The optimized query:

SELECT
        `start`.* 
    FROM
        `gearwise_estimation` 
    JOIN
        `catch_estimation` 
            ON `gearwise_estimation`.`estimationid` = `catch_estimation`.`estiamteid` 
            AND `year` = 2018 
    WHERE
        catch_estimation.month LIKE '%8%' ESCAPE '!' 
        AND catch_estimation.month LIKE '%9%' ESCAPE '!' 
        AND gearwise_estimation.gearname LIKE '%OBGN%' ESCAPE '!' 
        AND catch_estimation.centerid LIKE '%2%' ESCAPE '!' 
    ORDER BY
        `catch_estimation`.`month` ASC,
        `catch_estimation`.`centername` ASC