Option D: 'Strut' means 'walk with an arrogant (thinking highly of oneself) or conceited way'.
It means the same as the given expression. So, option D is correct.
Option A: 'Jog' means 'run at a steady gentle pace'.
Option B: 'Trek' means 'a long journey made on foot'.
Option C: 'Trudge' means 'walk slowly and with heavy steps'.
These words do not mean the same as the given expression. Hence options A, B and C are wrong.