They can give families like yours a sense of security going into the New Year.这里的非谓语做定语还是做状语呢，我认为是做定语。
They can give families like yours a sense of security going into the New Year.
本句，going into the New Year 作定语或作状语，均可。
1. 根据做定语理解：
我把直接宾语和间接宾语调换一下地方。
They can give a sense of security to families like yours going into the New Year. （作 failies 的后置定语）
2. 根据做状语理解：
They can give families like yours a sense of security when they go into the New Year.
going into the New Year，是目前分词短语作状语，具体说是时间状语。其逻辑主语，不是句子的主语，而是 families like yours。这就是所谓的“与与宾语有关的状语”。
【翻译】
他们/它们 可以给你如此的家庭一种安全感，迎接新年。
他们/它们 能叫你如此的家庭在度过新年时有安全感。
