This verse is part of a proposal from Shechem, the son of Hamor, to Jacob and his sons after Shechem violated Jacob's daughter Dinah. Let's break down what it means:

"Ask me a great amount for a dowry...": Shechem is offering to pay whatever bride price (dowry) Jacob and his sons demand for Dinah. In ancient Near Eastern culture, the bride's family received a payment from the groom's family. The amount of the dowry reflected the bride's value and status.
"...and I will give whatever you ask of me...": This is a clear indication that Shechem is deeply in love with Dinah and is willing to go to any lengths to marry her. He's essentially saying, "Name your price; I'll pay it."
"...but give me the young lady as a wife.": This is the core request. He wants to marry Dinah, and he's willing to compensate her family generously to make it happen.

In essence, the verse reveals Shechem's desire to marry Dinah and his willingness to pay a significant bride price to obtain her hand in marriage. It highlights the importance of bride price in ancient marriage customs and Shechem's apparent desperation to marry Dinah, even after having violated her.

Important Note: While Shechem is offering to legitimize the situation through marriage and payment, his initial act of violating Dinah was a serious offense. The passage in Genesis goes on to describe how Jacob's sons use this proposal to deceive and ultimately kill Shechem and his people. The verse highlights the complexities and cultural differences in how such situations were handled in ancient times.