Karnaugh Map from this expression?
Your K-Map is correct.

R = (X + X' + Y' + Z)(XY + X'Y'Z+YZ')
R = (1 + Y' + Z)(XY + X'Y'Z+YZ')
R = (1)(XY + X'Y'Z+YZ')
R = XY + X'Y'Z+YZ'
R = XYZ' + XYZ + X'Y'Z + XYZ' + X'YZ'
R = XYZ + X'Y'Z + XYZ' + X'YZ'

respective terms of last equation will be logic one in K-Map