I thought that you had already made other plans, so I didn't want to cause you any unnecessary burden by inviting you to my place.
ご質問ありがとうございます。
"I thought that you had already made other plans,"=「君が既に他の予定を立てていたのだと思った」
"so I didn't want to cause you any unnecessary burden"=「だから、君に余計な迷惑をかけたくなかった」
"by inviting you to my place."=「僕の家に誘うことで。」
ご参考に。