Prince Francis Ernest of Hesse-Darmstadt
Francis Ernest of Hesse- Darmstadt( born 25 January 1695 in Gießen; died: 8 January 1716 in Darmstadt) was a German nobleman.
He was the third son of Count Landgrave Ernest Louis of Hesse- Darmstadt( 1667 – 1739) from his marriage to Dorothea Charlotte( 1661 – 1705), daughter of the Margrave Albert of Brandenburg- Ansbach.
He replaced his brother Charles William of Hesse- Darmstadt as Colonel of the Hesse- Darmstadt Kreis Regiment when Charles William died during the War of Spanish Succession.
Princess Caroline of Hesse-Darmstadt
Caroline of Hesse-Darmstadt (2 March 1746, Buchsweiler – 18 September 1821, Homburg) was Landgravine consort of Hesse-Homburg by marriage to Frederick V, Landgrave of Hesse-Homburg.
She was the eldest daughter of Louis IX, Landgrave of Hesse-Darmstadt and his wife Caroline.
She married Frederick V, Landgrave of Hesse-Homburg on 27 September 1768.
The marriage was contracted for diplomatic and political reasons as the symbol of an inheritance dispute between their respective families.
Caroline and Frederick V produced many children but their marriage never developed into a personal relationship, and they lived mostly separated lives.
Caroline often spent time in the famed little villa that was given to her use in the forest near Homburg.
Philip of Hesse-Darmstadt
Philip of Hesse- Darmstadt( July 20, 1671 in Darmstadt – August 11, 1736 in Vienna) was a Prince of Hesse- Darmstadt, Imperial Field marshal and Governor of Mantua.
Prince Charles William of Hesse-Darmstadt
Karl Wilhelm of Hesse- Darmstadt( 17 June 1693, Nidda- 17 May 1707, Gießen) was a Prince of Hesse- Darmstadt.
Caroline of Hesse-Homburg
Caroline of Hesse- Homburg( 1771 – 1854) was the daughter of Frederick V, Landgrave of Hesse- Homburg and his wife, Caroline of Hesse- Darmstadt.
She married in 1791 to Louis Frederick II, Prince of Schwarzburg- Rudolstadt.
They had seven children together.
Caroline died on 20 June 1854.
Louis VI, Landgrave of Hesse-Darmstadt
Louis VI of Hesse-Darmstadt  (25 January 1630 – 24 April 1678) was Landgrave of Hesse-Darmstadt from 1661 to 1678.
He was the eldest of three sons of the Landgrave George II of Hesse-Darmstadt and Sophia Eleonore of Saxony.
Landgravine Auguste of Hesse-Homburg
Landgravine" Auguste" Fredericka of Hesse- Homburg( full German name:" Auguste Friederike, Landgräfin von Hessen- Homburg"; 28 November 1776, Bad Homburg vor der Höhe, Landgraviate of Hesse- Homburg, Holy Roman Empire – 1 April 1871, Ludwigslust, Grand Duchy of Mecklenburg- Schwerin), was a member of the House of Hesse and a Landgravine of Hesse- Homburg by birth.
Through her marriage she was also a member of the House of Mecklenburg and Hereditary Grand Duchess of Mecklenburg- Schwerin.
She was the sixth child and fourth daughter of Frederick V, Landgrave of Hesse- Homburg and his wife Landgravine Caroline of Hesse- Darmstadt, in turn daughter of Louis IX, Landgrave of Hesse- Darmstadt.
Prince George Charles of Hesse-Darmstadt
George Charles( German:" Georg Karl") of Hesse- Darmstadt( 14 June 1754- 28 January 1830, Schüttrisberg, now in Slovakia) was a German prince of the House of Hesse- Darmstadt.
He was the fourth child and third son of Prince George William of Hesse- Darmstadt and Countess Maria Louise Albertine of Leiningen- Dagsburg- Falkenburg.
Countess Palatine Caroline of Zweibrücken
Caroline of the Palatinate-Zweibrücken (Henriette Caroline Christiane Louise; 9 March 1721 – 30 March 1774) was Landgravine of Hesse-Darmstadt by marriage to Louis IX, Landgrave of Hesse-Darmstadt.
She was famed as one of the most learned women of her time and known as The Great Landgräfin.
Louis IX, Landgrave of Hesse-Darmstadt
Louis IX of Hesse-Darmstadt  (15 December 1719 – 6 April 1790) was the Landgrave of Hesse-Darmstadt from 1768 - 1790.
He was a son of Louis VIII, Landgrave of Hesse-Darmstadt, and Charlotte of Hanau-Lichtenberg and Müntzenberg.
He was born in Darmstadt on 15 December 1719.
On 12 August 1741, Louis married Caroline of Zweibrücken, daughter of Christian III, Duke of Zweibrücken.
They had three sons and five daughters, including:
In 1775, Louis married Marie Adelaide of Cheirouze, countess of Lemberg.
On 6 April 1790 Louis died in Pirmasens.

Question: Who is the paternal grandfather of Princess Caroline Of Hesse-Darmstadt?
Answer: Louis VIII, Landgrave of Hesse-Darmstadt