The number of straight lines that are equally inclined to the three-dimensional coordinate axes is:

Let the direction cosines of a line be $l,m,n$.The line is equally inclined to the axes, so $|l|=|m|=|n|$.We know $l^2+m^2+n^2=1$.$3l^2=1⟹l=\pm \frac{1}{\sqrt{3}}$.Thus, $l,m,n\in \left\{\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}\right\}$.Possible combinations of $(l,m,n)$ are:$\left(\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}\right)$$\left(-\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}\right)$$\left(\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}\right)$$\left(\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}\right)$ (The negatives of these represent the same lines).Total distinct lines = $4$.