Not sure what you're after - you don't necessarily need an 'ON' to do a JOIN but perhaps you do need to define the tables.  I don't know which columns belong to which tables (and neither does mysql, perhaps that's the problem)
Assuming that 'member_id' is in exp_member_data and 'col_id_12' is in exp_channel_grid_field_11, you probably need to do something like this:  
SELECT COUNT(*)
 FROM exp_channel_grid_field_11
 INNER JOIN exp_member_data
 WHERE `exp_channel_grid_field_11.col_id_12` = 'Race'
 && `exp_member_data.member_id` = '1'  
and you can "pretty it up" with "table aliases" such as like this:  
SELECT COUNT(*)
 FROM exp_channel_grid_field_11 e11
 INNER JOIN exp_member_data ed
 WHERE `e11.col_id_12` = 'Race'
 AND `ed.member_id` = '1'   
Or, maybe there should be an 'ON' member_id?  
SELECT COUNT(*)
 FROM exp_channel_grid_field_11 e11
 INNER JOIN exp_member_data ed  
 ON e11.member_id = ed.member_id  
 WHERE `e11.col_id_12` = 'Race'
 AND `ed.member_id` = '1'