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'