On Thursday evening Wellington attended a ball given by the Duchess of Richmond in Brussels and it wasn't until the early hours of Friday the 16th that he gave orders to concentrate the Anglo-Dutch army at Quatre-Bras. Prince Orange was ordered to hold Quatre-Bras until the rest of the army arrived.
Wellington's strategy was to stay in contact with the Prussians at Ligny where the combined armies could defeat Napoleon. Napoleon's goal was to prevent the allied armies from supporting each other and crush one of them with overwhelming superiority of numbers. As it turned out, neither strategy succeeded on Friday, June 16th.
Ney held the Anglo-Dutch troops at bay around Quatre-Bras in a tough battle with heavy losses. He eventually took the crossroads at Quatre-Bras only to be driven back when Wellington arrived with fresh troops. Meanwhile, Napoloeon attacked the Prussians at Ligny with Grouchy's corps and the reserve that had been under his personal command. The Prussians were defeated but not destroyed [Battle of Ligny].
Waterloo: Myth and Reality]
Now comes one of the decisive moments of the Waterloo campaign. Blücher's Prussians retreated in orderly fashion on Wavre where he could remain in touch with Wellington who was forced to fall back to Wavre after the position at Quatre-Bras became untenable. Grouchy was ordered to pursue Blücher and prevent the Prussians from supporting the Anglo-Dutch army. Grouchy failed to do this because his corps did not move quickly and was confused about the direction of the Prussian retreat. As we shall see, Grouchy's failure is blamed for the defeat at Waterloo two days later.
Meanwhile, Wellington was able to fall back to a defensive position at Waterloo where he waited for the French army.
Battle of Ligny]
Summoned to Waterloo: Brussels, dawn of June 16, 1815 by Robert Alexander Hillingford. Officers leaving the Duchess of Richmond's ball.
Quatre Bras (Black Watch at Bay) by William Barnes Wollen