6. Given that the angle formed by skew lines $a$ and $b$ is $50^{\circ}$, and $P$ is a fixed point in space, then the number of lines passing through point $P$ and forming angles of $52^{\circ}$ with both $a$ and $b$ is $\qquad$ lines.
As shown in the figure, draw lines $a^{\prime} / / a, b^{\prime} / / b$ through point $P$, then the angle formed by $a^{\prime}, b^{\prime}$ is $50^{\circ}$. It is easy to know that there are only two lines $m, n$ passing through point $P$ and forming angles of $52^{\circ}$ with both $a^{\prime}, b^{\prime}$. Therefore, there are only 2 lines passing through point $P$ and forming angles of $52^{\circ}$ with both $a, b$.