This word consists of the kun'yomi reading for 茨, and exception for 城 and the on'yomi for 県. Phew! You haven't learned this weird reading for 城 yet, so here's a mnemonic to help you:
Ibaraki prefecture is famous for making keys (き)! It's their biggest export. The key to knowing this reading is in the keys they make! Or, just knowing that it's the same in English and Japanese.
My parents’ home is in Ibaraki prefecture.