Can you help me resolve a ORA-01006?

Missing colon, here: ...   || lv_dbname

You are passing 3 variables (using ,,)  and defined 2 in your query :lv.

You can't pass however the databaselink name as a bind variable, so you must include it in the query text.

Try
lv_dbname := ' 'LINK_ABCDEF ';
EXECUTE IMMEDIATE
            'select  oldest_backup_time,newest_backup_time  into :lv_oldest, :lv_newest from '
            || lv_dbname
            || '.'
            || 'rc_backup_set_summary'
            || '@'
            || lv_dbname
            USING lv_oldest,lv_newest;

Is the schema name same as dblink ?

Try

EXECUTE IMMEDIATE
            'select  oldest_backup_time,newest_backup_time  into :lv_oldest, :lv_newest from '
            || lv_dbname
            || '.'
            || 'rc_backup_set_summary'
            || '@'
            || 'LINK_ABCDEF '
            USING lv_oldest,lv_newest;

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1) Your query does not have and conditions and therefore will none of the posted variations will work unless the table has ONE row.

2) In the EXECUTE IMMEDIATE statement, the "USING" part is to supply bind variable values to the query and the "INTO" part is to receive results from the query.

3) Other than variables, in order to supply information that builds the query and which is contained in variables (like schema and/or table name and/or database link. etc...), you must CONCATENATE these variables to the query  text.

hi flow, the schema name is not same as the link name, i tried to use the link name as a variable, but your script did not work...
hi mikeom_dba, i tried your scipt, and it worked thank you...

thank you..