We've got the following system $$ \begin{split} 10^{33}X &\equiv 47 \pmod{51} \\ 4^{62} &\equiv 8 \pmod{9} \end{split} $$
And I've managed to rewrite this as $$ \begin{split} X &\equiv 2 \pmod{3} \\ X &\equiv 3 \pmod{17} \\ X &\equiv 35 \pmod{9} \end{split} $$
However I'm not sure how to follow on this. Any help with this would be appreciated, thanks!
Note first that $X\equiv8\pmod{9}$ and this condition implies the first one $X\equiv2\pmod{3}$.
Hint: Try to find two numbers $X_1,X_2$ such that $$\begin{matrix}X_1&\equiv 1\pmod{9}\\X_1&\equiv 0\pmod{17}\end{matrix}\qquad\begin{matrix}X_2&\equiv 0\pmod{9}\\X_2&\equiv 1\pmod{17}\end{matrix}$$ Then $X=8X_1+3X_2\pmod{9\times17}$.