香港給我一個永久記憶..英文係咩?

Hong Kong gave me an eternal memory.
"gave me" should be followed by a noun.

Hong Kong makes me to have the permanent memory

I have got a unforgettable mermory in Hong Kong.

I got a permanent remembrance from living in Hong Kong. (or ...visiting in HK. 要按文意而定, 主角是我, 如果 HK 做主角, 就很不順眼, 英文是倒轉用詞的.)

Hong Kong gives me an eternal/ a perpetual/ an everlasting memory.
HONG KONG gave me to have eternity 这句话错, 是因为give 不作使动用法, 应该换成let, remember是动词, 不能当名词用.
可改为 Hong Kong lets/let me to have an eternal/ a perpetual/ an everlasting memory.
而用lets/let, 取决于时态, 前者为一般现在时, 后者为一般过去时.

Hong Kong gives me an everlasting memory.
'eternity' 係名詞，'remember' 係動詞
但'everlasting' 係形容'memory'
所以'everlasting' 應該要用形容詞，而'memory' 用名詞

Hong Kong is always on my mind