解析：∵y=2sin(4x+φ）+2,对称轴x=π/3
对称轴：4x+φ=2kπ+π/2==>4x=2kπ+(π-2φ)/2==>x=kπ/2+(π-2φ)/8
令(π-2φ)/8=π/3==>φ/4=π/8-π/3=-5π/24==>φ=-5π/6
4x+φ=2kπ-π/2==>4x=2kπ-(π+2φ)/2==>x=kπ/2-(π+2φ)/8
令-(π+2φ)/8=π/3==>φ/4=-π/8-π/3=-11π/24==>φ=-11π/6
∴φ=-5π/6或φ=-11π/6