Could someone explain this sentence in simple English please?

You can understand what you write.

I can only assume that it means our handwriting should be readable and not written sloppily...?

If he learns to write from left to right, as in English, he will also read from left to right, and if he learns to write from right to left, as in Arabic, he will also read from right to left.
IF I AM NOT MISTAKEN, OLDPROF HAD A DIFFERENT ANSWER BEFORE, BUT NOW HIS ANSWER IS VERY SIMILAR TO MINE.

It is a horrible ambiguous sentence. But I think it's trying to say:

If he learns to write right to left, he'll learn to read in that direction too. But if he learns to write left to right, that's the direction he'll learn to read.