This is the 4449th most frequent Japanese word.
多大
"多大" means "great" or "immense."
In this sentence, "多大な" is used as an adjective to describe "ご支援" (support) as being significant or great in amount.
多大なご支援をいただき、誠にありがとうございます。
Thank you very much for your tremendous support.
Here, "多大な" serves as an adjective to emphasize the extent or volume of "努力" (effort) as being considerable.
彼の成功には多大な努力が隠れていました。
His success hid tremendous effort.
"多大な" in this sentence characterizes "時間" (time), highlighting that the project required a substantial time investment.