No...... the period is determined by setting 4x to 2pi and solving for x...so we have
4x = 2pi divide both sides by 4
x = pi/2 = the period
This makes sense.......the normal period of the sine graph is "compressed" by a factor of 4.....see the normal graph and the graph of y = sin 4x here : https://www.desmos.com/calculator/aqkipoldkg
Note that there are 4 periods in 2pi ...so.... each period has a length of pi/2