Explanation:
( Check attachment for the design )
When capacitor is charging
[tex]V_{c} = V_{cc} ( 1- e^{\frac{t}{Rc} })[/tex]
At
t = [tex]t_{0}[/tex]
[tex]V_{C}[/tex] becomes [tex]\frac{2V_{cc} }{3} = V_{cc} ( 1- e^{\frac{-t0}{Rc} } )[/tex]
[tex]\frac{e^{t0} }{Rc} = 3[/tex]
[tex]T_{0} = 1.1 Rc[/tex]
[tex]T_{0} = 12 = 1.1 Rc[/tex]
Rc = 10.909
So , Assume R = 10 MΩ
C = 1.0909 μ F