The term shitakitae (kanji: 下鍛え) means "hammering in forging" in English. It is written したきたえ in hiragana. It's pronounced roughly like "she-tah-key-tah-eh".
This refers to the first step in the forging (鍛え, kitaeKITAE 鍛え "forge" learn more...) process whereby the swordsmith begins to hammer the steel. This is followed by the orikaeshi tanrenORIKAESHI TANREN 折り返し鍛錬 "folding step in forging" learn more... (折り返し鍛錬) and the agekitae (上げ鍛え) processes.
上, by itself, is pronounced ue and means up or above. 下, pronounced shita on its own, means down or below. In the case of shitakitae, 下 is used in the special sense of before, similar to its use in the word for preparation (下準備, shitajunbi).
鍛える, kitaeru, is a verb meaning to build up (the body), to undergo training (in a skill, especially athletic), or to strengthen (one’s mind).