Answer:   80 different ways.

Start with the R in the top left-hand corner.
Go to the A on the right.
Now go straight on to the D.
You can now complete the word in four ways, because there are four A's available through which you may reach an R.
 
There are four ways of reading through the right-hand A.
There are the same number of ways through the A that is immediately below the starting point.
The total is now eight.

If you take the third route diagonally through the A, you will have the option of using any one of the three D's,
You may now complete the word in four ways.

You can spell RADAR in twelve ways through the diagonal A.

Twelve plus eight equals twenty readings, that all start from the R in the top left-hand corner.

The four corners are equal.
Four times twenty equals eighty different ways of spelling RADAR