If the form is for a trade mark or design, then anm. bkg. or anmeldelsesbekendtgørelse probably refers to "(date of) publication of the application". It refers to the date on which the application was published in the Trademark Gazette prior to registration. Compare this list of codes:
(442) Date of publication of the application Bekendtgørelsesdato (last page)
http://www.dkpto.dk/publikationer/tidender/vtid0132_150801.p...

See also:
Publication
If we find no hindrances for the registration of your mark, we issue a registration certificate, which is sent to you. At the same time, we publish the mark in the Danish Trademark Gazette. During the subsequent opposition period of two months, others may file an opposition against your mark. If no opposition is filed, you will receive a final statement about your registration.
http://iprights.dkpto.org/trademark/our-examination-of-your-...