Confine your attention to the L in the top left-hand corner. 
Suppose you go by way of the E on the right: you must then go straight on to the V, from which letter the word may be completed in four ways, for there are four E's available through which you may reach an L. 
There are therefore four ways of reading through the right-hand E. 
It is also clear that there must be the same number of ways through the E that is immediately below our starting point. 
That makes eight. 
If, however, you take the third route through the E on the diagonal, we then have the option of any one of the three V's, by means of each of which you may complete the word in four ways. 
You can therefore spell LEVEL in twelve ways through the diagonal E. 
Twelve added to eight gives twenty readings, all emanating from the L in the top left-hand corner; and as the four corners are equal, the answer must be four times twenty, or eighty different ways.