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.

Optimal indexes for this query:

CREATE INDEX gl_combinations_idx_enabled_fl_chart_id_segment1 ON gl_code_combinations (enabled_flag,chart_of_accounts_id,segment1);
CREATE INDEX gl_combinations_idx_enabled_fl_chart_id_segment2 ON gl_code_combinations (enabled_flag,chart_of_accounts_id,segment2);
CREATE INDEX gl_combinations_idx_enabled_fl_chart_id_segment3 ON gl_code_combinations (enabled_flag,chart_of_accounts_id,segment3);
CREATE INDEX gl_combinations_idx_enabled_fl_chart_id_segment4 ON gl_code_combinations (enabled_flag,chart_of_accounts_id,segment4);
CREATE INDEX gl_combinations_idx_enabled_fl_chart_id_segment5 ON gl_code_combinations (enabled_flag,chart_of_accounts_id,segment5);
CREATE INDEX gl_combinations_idx_enabled_fl_chart_id_segment6 ON gl_code_combinations (enabled_flag,chart_of_accounts_id,segment6);
CREATE INDEX gl_combinations_idx_enabled_fl_chart_id_segment7 ON gl_code_combinations (enabled_flag,chart_of_accounts_id,segment7);
CREATE INDEX gl_combinations_idx_enabled_fl_chart_id_segment8 ON gl_code_combinations (enabled_flag,chart_of_accounts_id,segment8);

The optimized query:

SELECT
        (SELECT
            SUM(COUNT(DISTINCT gl_code_combinations.segment1)) 
        FROM
            gl_code_combinations 
        WHERE
            gl_code_combinations.enabled_flag = 'Y' 
            AND gl_code_combinations.chart_of_accounts_id = 50181 
        GROUP BY
            gl_code_combinations.segment1) unique_segment1,
        (SELECT
            SUM(COUNT(DISTINCT gl_code_combinations.segment2)) 
        FROM
            gl_code_combinations 
        WHERE
            gl_code_combinations.enabled_flag = 'Y' 
            AND gl_code_combinations.chart_of_accounts_id = 50181 
        GROUP BY
            gl_code_combinations.segment2) unique_segment2,
        (SELECT
            SUM(COUNT(DISTINCT gl_code_combinations.segment3)) 
        FROM
            gl_code_combinations 
        WHERE
            gl_code_combinations.enabled_flag = 'Y' 
            AND gl_code_combinations.chart_of_accounts_id = 50181 
        GROUP BY
            gl_code_combinations.segment3) unique_segment3,
        (SELECT
            SUM(COUNT(DISTINCT gl_code_combinations.segment4)) 
        FROM
            gl_code_combinations 
        WHERE
            gl_code_combinations.enabled_flag = 'Y' 
            AND gl_code_combinations.chart_of_accounts_id = 50181 
        GROUP BY
            gl_code_combinations.segment4) unique_segment4,
        (SELECT
            SUM(COUNT(DISTINCT gl_code_combinations.segment5)) 
        FROM
            gl_code_combinations 
        WHERE
            gl_code_combinations.enabled_flag = 'Y' 
            AND gl_code_combinations.chart_of_accounts_id = 50181 
        GROUP BY
            gl_code_combinations.segment5) unique_segment5,
        (SELECT
            SUM(COUNT(DISTINCT gl_code_combinations.segment6)) 
        FROM
            gl_code_combinations 
        WHERE
            gl_code_combinations.enabled_flag = 'Y' 
            AND gl_code_combinations.chart_of_accounts_id = 50181 
        GROUP BY
            gl_code_combinations.segment6) unique_segment6,
        (SELECT
            SUM(COUNT(DISTINCT gl_code_combinations.segment7)) 
        FROM
            gl_code_combinations 
        WHERE
            gl_code_combinations.enabled_flag = 'Y' 
            AND gl_code_combinations.chart_of_accounts_id = 50181 
        GROUP BY
            gl_code_combinations.segment7) unique_segment7,
        (SELECT
            SUM(COUNT(DISTINCT gl_code_combinations.segment8)) 
        FROM
            gl_code_combinations 
        WHERE
            gl_code_combinations.enabled_flag = 'Y' 
            AND gl_code_combinations.chart_of_accounts_id = 50181 
        GROUP BY
            gl_code_combinations.segment8) unique_segment8 
    FROM
        DUAL