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Forty-five year-old Korean-American Kenneth Bae was arrested in 2012.

I think the hyphen is wrong. It should be "Forty-five-year-old" or "45-year-old". So I wonder how to use the hyphen.

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According to the Chicago Manual of Style you are right and it should be "Forty-five-year-old [man]". Quoting from the Chicago Manual of Style (14th edition, page 223):

two-year-old car
sixty-five-year-old man
two-and-a-half-year-old child
six-year-old girls
six year-old girls
man sixty-five years old
child two and a half years old
twenty-four boys five years old

Adjective compounds comprising a number and a unit of measure are hyphenated before a noun. When an adjective is added after the unit of measure, the adjective and unit are joined by a hyphen. When the adjectival compound is preceded by another, modifying number, the hyphenated compound is kept separate from that number. if the compound comes after the noun, it may usually be left open, but in that case the unit is plural if the number is greater than one.

On the internet I have found this page to sum it up:

Hyphenate ages when they are adjective phrases involving a unit of measurement: “Her ten-year-old car is beginning to give her trouble.” A girl can be a “ten-year-old” (“child” is implied). But there are no hyphens in such an adjectival phrase as “Her car is ten years old.”

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The original phrase (forty-five year-old) is definitely incorrect. "Year-old" would imply a one year old, and the "forty-five" before it would only add confusion. I have seen it "forty-five year old" but adding two hyphens is fine. By the way, you would say, "Bae is forty-five years old", not "Bae is forty-five-years-old". –  Phil Perry Mar 3 at 14:33
    
@PhilPerry So you are just saying you agree with The Chicago Manual of Style quoted above? Or have I missed something in your comment? –  Laure Mar 3 at 16:29
    
I think you missed something. The CMoS is fine, though I personally disagree with some of their rules. I was partly responding to the OP, and partly to yours. "forty-five year old" is common usage, and "forty-five-year-old" (CMoS) is also common. –  Phil Perry Mar 3 at 17:57

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