Denmark passport holders are exempt of visa to Hk for 90 days. You can go to Hk firstly and then apply for the visa to Beijing from the Visa Office of the Commissioner of the Ministry of Foreign Affairs of the People's Republic of China in Hong Kong SAR.
Address: 7th Floor, Lower Block, China Resources Building,
No.26, Harbor Road, Wanchai
Open 09:00 to noon, and 14:00 to 17:00, Mon to Fri (except Hong Kong public holidays)
Do not take large baggage as you are not allowed to take it inside.

Enquiry Service
Tel- Enquiry
24 hour Automatic Answering Telephone: 852-34132300
Live Answering Telephone: 852-34132424 (available at 10:00-11:00, 15:00-16:00 on workdays)
Fax: 852-34132312
Email: mfa.gov.cn|fmcovisa_hk
Website: http://www.fmcoprc.gov.hk/eng/