The rocket fuel is made up of carbon, hydrogen and nitrogen. The molar mass of the fuel is 60.1 g/mole.
Let the molecular formula of the fuel be C(a)N(b)H(c) and let us assume that the nitrogen is not oxidized when the fuel burns.
When 2.859 g of the fuel is burnt we have 4.19 g of carbon dioxide and 3.428 g of water produced.
2.859 g of the fuel is approximately 0.04757 mole of the fuel
4.19 g of carbon dioxide has (4.19/44.01) = 0.0952 mole of C
3.428 g of water has 2*3.428/18.02 g = 0.3804 mole of hydrogen
We have 0.0952 mole of carbon in 0.04757 mole of the fuel. 0.0952/ .04757 = 2 approximately. This gives 2 atoms of carbon in one molecule of the fuel.
We have 0.3804 mole of hydrogen in 0.04757 mole of the fuel. .3804/.04757 = 8 approximately. This gives 8 atoms of hydrogen in one molecule of the fuel.
The rest of the fuel is nitrogen, or one molecule of the fuel has (60.1 - 8*1.008 - 12*2)/14.01 = 2 atoms of nitrogen
So the molecular formula of the fuel is C(2)N(2)H(8).