How to get the get the select values created by ACF plugin in wordpress

In this bit of code:

$field = get_field_object('field_51d3f9c3f5554');

$field['choices'] will contain an array of the available choices for that field, not the currently selected value, $field['value'] contains the currently selected value.

However, using get_field_object when all you want is the currently selected value is unnecessary.

for the correct use of get_field(), read the documentation carefully to learn what you must pass to that function, specifically the $post_id examples section. taxonomy terms are not the same as posts, you have to pass an additional argument in the form of "$taxonomy_$term_id".

EDIT- also note, in your call to get_field(' select_to_display_'), you have a space before the key name, which will fail unless the key is actually prefixed with a space, which I presume is not the case.