Custom Date Fields in Types store Timestamps, wich are seconds from the Timestamp Start moment.
So it can not really be said, this is a month and this a day and so on.
It's all calculated in seconds from xy.
But it should be possible to adapt Minesh's Code.
What he does, he creates 3 variables:
//This is the Value saved in the Database (your Date Field)
$val = get_post_meta( $post->ID, 'wpcf-ordination', true );
//This is the month value, got from the above "full date". We get the month with 'n'. It's a number from 1 to 12
$mon = date('n',$val);
//Same here, this is the day, number of the day in the month, without leading 0
$day = date('j',$val);
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So, what you need is to change the above $mon and $day variables and pass the number you exactly need.
Since you have a max and min value, you just need to compare those with a proper date format in PHP.
Like:
$val = get_post_meta( $post->ID, 'wpcf-ordination', true );
$mon = date('n',$val);//get month
$day = date('j',$val);//get day
$min_day = 1;
$max_day = 31;
$min_month = 6;
$max_monh = 9;
Then you compare if the $mon and day are greater or equal, and smaller or equal to your above set new variables (min and max)