Since there is no direct transportation from Delhi to Shouguang, it is suggested that you make a transfer at Beijing City(https://www.travelchinaguide.com/cityguides/beijing.htm).

Firstly, from Delhi, you should take an international flight to arrive at Beijing Capital Airport(https://www.travelchinaguide.com/cityguides/beijing/capital-airport.htm).

Second, you have to get to Beijing South Railway Station and then take a high-speed train to Weifang City(https://www.travelchinaguide.com/cityguides/shandong/weihai/) of Shandong. The train will take about 4.5 hours. Sugggested that you book the Beijing train tickets(https://www.travelchinaguide.com/china-trains/beijing-schedule.htm) in advance.

Finally, you could take a coach from Weifang to Shouguang in 1.5 hours.

Thanx. Sam,
Can I take a flight from Beijing to Shandong to avoid the train & coach travelling of 6 hrs.

Yes, you could take a Beijing flight(https://www.travelchinaguide.com/china-flights/cheap-beijing-flights.htm) to Weifang Airport in one hour and then proceed to Shouguang.