Let us go through each of the choices one by one.
(a).
A rotation 90 degree clockwise followed by a translation 3 units down.
This Lands the L'M'N' into the first quadrant and L'N' is now parallel to the y-axis; therefore, this transformation leaves the corresponding sides not being parallel to the same axis and hence is the correct option to choose.
(b).
A translation 4 units to the left followed by a reflection over the y-axis.
A translation of 4 units to the left leaves the sides parallel and the reflection over the y-axis also leaves the sides parallel; therefore, this is not the correct option to choose.
(c).
A reflection over the x-axis followed by a dilation by a factor of 2 about the origin.
The reflection over the x-axis leaves the sides parallel and dilation by a factor of 2 just bloats the figure - it does not change the angle of sides with respect to the x and y axes; therefore, this choice is also not the correct one to choose.
(d).
A dilation by a factor of 0.25 about the origin followed by a 180° rotation clockwise about the origin.
The dilation by a factor of 0.25 shrinks the triangle, and the 180° rotation clockwise leaves the side L'M' parallel to the x-axis - the same as it was before; therefore, this is not the correct choice to choose.
Hence, the correct option is A.