jmc

If Marika is 8 years old, and her father is four times her age, then her father is $4\cdot 8=32$ years old. So now $x$ years after 2004, Marika will be $8+x$ years old and her father will be $32+x$ years old. If the father's age is three times Marika's age then: $$\begin{array}{rl}32+x& =3(8+x)\\ 32+x& =24+3x\\ 2x& =8\\ x& =4\end{array}$$So the year is $2004+4=\boxed{2008}$.