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calculista
the correct question is
Radius of outer circle is 2x radius of inside circle is 6 cm. Area of shaded region is 288pi cm2. What is the value of x

we know that

[the area of a circle]=π*r²

for the outer circle area
r=2x
Area=π*(2x)²---------> 4πx² cm²

for the inside circle area
r=6 cm
Area=π.6²=36π cm²

[shaded region]=288π cm²
[shaded region]=[the outer circle area] - [the inside circle area] 
[shaded region]=[4πx²] - [36π] 
288π=[4πx²] - [36π] ------> 288π+36π=4πx²-----> x²=324/4----> 81
x=9 cm

the answer is x=9 cm

see the attached figure


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