That explanation seems a bit complicated. If he's growing at a constant rate, then we can assume he grows g inches per year. Then in inches, his heights on each birthday are:
12th bday: 54
13th bday: 54 + g
14th bday: 54 + 2g
15th bday: 54 + 3g
We know his height on his 15th birthday is 20% greater than on his 13th birthday. If one thing is 20% greater than another, it is 1.2 times the other. So we get an equation:
54 + 3g = 1.2(54 + g)
270 + 15g = 6(54 + g)
270 + 15g = 324 + 6g
9g = 54
g = 6
I multiplied both sides by 5 to get rid of decimals in the second step, but that's not necessary if you're happy working with decimals.
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