Number of days?

Let the work mentioned in the problem be $W$ and the rates of doing work of a man and woman be $m$ and $w$ respectively. Then we have:

$\begin{cases} 3 \times 15 m = 45 m = W & \implies m = \dfrac W{45} \\ 6 \times 15 w = 90 w = W & \implies w = \dfrac W{90} \end{cases} \implies m = 2w$

And:

$\begin{aligned} 2\times 3m + 3x w & = \color{#3D99F6} W & \small \color{#3D99F6} \text{Note that }W=90w \\ {\color{#D61F06}6m} + 3x w & = \color{#3D99F6} 90w & \small \color{#D61F06} \text{Note that }m=2w \\ {\color{#D61F06}12w} + 3xw & = 90w \\ \implies x & = \frac {90-12}3 \\ & = \frac {78}3 \\ & =\boxed{ 26} \end{aligned}$