(A)                 (B)
      

The period of a function is the number of units along the x-axis
that span one complete cycle of the graph, where one complete
cycle is either
 or  or  or 

As you see in the first graph (A), the cycle begins at -4 on
the x-axis and the cycle doesn't end until +4 on the x axis.
From -4 to +4 on the x-axis is a span of (+4)-(-4) = +4+4 = 8
units, so the period of the (A) graph is 8.

On graph (B), there are two complete cycles like this  
over the same span on the x-axis. Therefore the number of units on the 
x-axis that is spanned by just one cycle  is 4.
So the period of the (B) graph is 4.

Edwin