In 1989 the reverse design of the Lincoln Cent was modified and is identified mainly by the designer initials “FG”. It is not certain why this occurred but it’s obvious mint employees used the normal 1988 Lincoln Cent obverse working dies paired with the new 1989 modified reverse working dies.
The 1989 Lincoln Cent FG is identified by the outside leg of the G extending down past the bottom of the letter. The inner curve of the G also extends into the middle of the opening in the G. 1988 Lincoln Cent With 1989 Reverse is worth $10 to $30 in circulated grades but can be worth $100 or more in mint state grades.
What you look for is the 1989 reverse in the image above on the reverse of a 1988 no mint (Philadelphia Mint) mark or D (Denver Mint) mint mark Lincoln Cent.
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Sources: Lincoln Cent Resource, Wexler’s doubledie.com