The optimization process and recommendations:

1. 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.
2. 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.
3. Explicitly ORDER BY After GROUP BY (modified query below): By default, the database sorts all 'GROUP BY col1, col2, ...' queries as if you specified 'ORDER BY col1, col2, ...' in the query as well. If a query includes a GROUP BY clause but you want to avoid the overhead of sorting the result, you can suppress sorting by specifying 'ORDER BY NULL'.
4. Prefer Sorting/Grouping By The First Table In Join Order (modified query below): The database can use indexes more efficiently when sorting and grouping using columns from the first table in the join order. The first table is determined based on the prediction of the the optimal first table, and is not necessarily the first table shown in the FROM clause.

Optimal indexes for this query:

ALTER TABLE `assign_job` ADD INDEX `assign_job_idx_employee_id` (`employee_id`);
ALTER TABLE `emp_skills` ADD INDEX `emp_skills_idx_employee_id` (`employee_id`);
ALTER TABLE `employee` ADD INDEX `employee_idx_employee_id` (`employee_id`);
ALTER TABLE `employment` ADD INDEX `employment_idx_employee_id` (`employee_id`);
ALTER TABLE `ml_designations` ADD INDEX `ml_designations_idx_ml_id` (`ml_designation_id`);
ALTER TABLE `ml_projects` ADD INDEX `ml_projects_idx_project_id` (`project_id`);
ALTER TABLE `ml_skill_type` ADD INDEX `ml_type_idx_skill_id` (`skill_type_id`);
ALTER TABLE `position_management` ADD INDEX `position_managemen_idx_current_employement_id` (`current`,`employement_id`);

The optimized query:

SELECT
        * 
    FROM
        (`emp_skills` ES) 
    INNER JOIN
        `employee` E 
            ON `E`.`employee_id` = `ES`.`employee_id` 
    INNER JOIN
        `ml_skill_type` MLST 
            ON `MLST`.`skill_type_id` = `ES`.`ml_skill_type_id` 
    INNER JOIN
        `employment` ET 
            ON `ET`.`employee_id` = `E`.`employee_id` 
    INNER JOIN
        `position_management` PM 
            ON `PM`.`employement_id` = `ET`.`employment_id` 
            AND PM.`current` = 1 
    INNER JOIN
        `ml_designations` MLD 
            ON `MLD`.`ml_designation_id` = `PM`.`ml_designation_id` 
    LEFT JOIN
        `assign_job` AJ 
            ON `AJ`.`employee_id` = `E`.`employee_id` 
    LEFT JOIN
        `ml_projects` MLP 
            ON `MLP`.`project_id` = `AJ`.`project_id` 
    GROUP BY
        `ES`.`employee_id` 
    ORDER BY
        NULL