The normal direction of writing for ancient Egyptian was right-to-left, which may be due to the use of papyrus rolls. But the pictorial nature of the hieroglyphs allowed them to be easily reversed. So, the texts could be written in both directions, with, however a preference for right-to-left.
Normally, the hieroglyphs that represent animated beings look toward the beginning of the text. So:
is to be read left-to-right, but
is to be read right-to-left
When the text goes along with representations, its orientation is the same as the one of the figure it accompanies. For example, when a stela is carved with a king making offerings to a god, the god is usually placed on the left, looking to the right, according to the normal orientation for hieroglyphs; the caption and discourses of the god are likewise turned right-to-left. The king making offering is on the right, turned toward the left, and his caption and discourses are turned left-to-right. See for example figure 2.
Of course, when symmetry is wanted (for example, you might find two stelas on each side of a doorway), this system allows inscriptions to be mirrored.
A side effect of this is that the normal orientation for a representation is as thought it was viewed turned towards the right. In such cases, if the representation is shown walking, the most advanced leg must be the left leg, because otherwise it would be partially hidden by the right leg. So, as Egyptian statues were mainly big hieroglyphs, they normally advance the left leg. See for example the figure of Amon on figure 2, or the funerary statue of Mereruka . In the inscription of figure 1, the sign ankh, ,to be read as ``may ... live'', is shared between two different name of the king Ramses III, one written right-to-left and the other left-to-right . As the sign is symmetric, this is often used. The text translate, left-to-right, beginning with ankh :
May the perfect god Heqa-maat-re liveand right to left :
May the son of Re, Ramses-[Heqa-Iunu] live