To solve this problem, we need to identify the correct combination of gases and conditions used by S.L. Miller in his experiment to produce amino acids.$\newline$Let's analyze the options:$\newline \bullet$Option 1: $$CH$_3,$H$_2,$NH$_4$ and water vapor at $800^\circ$C$\newline$ - This option is incorrect because it mentions $$CH$_3$ and $$NH$_4,$ which were not used in Miller's experiment.$\newline \bullet$Option 2: $$CH$_4,$H$_2,$NH$_3$ and water vapor at $600^\circ$C$\newline$ - This option is incorrect because the temperature is not the one used in Miller's experiment.$\newline \bullet$Option 3: $$CH$_3,$H$_2,$NH$_3$ and water vapor at $600^\circ$C$\newline$ - This option is incorrect because it mentions $$CH$_3,$ which was not used in Miller's experiment.$\newline \bullet$Option 4: $$CH$_4,$H$_2,$NH$_3$ and water vapor at $800^\circ$C$\newline$ - This option is correct. S.L. Miller used methane (CH$_4$), hydrogen (H$_2$), ammonia (NH$_3$), and water vapor at a high temperature of $800^\circ$C to simulate early Earth conditions and successfully produced amino acids.$\newline$Therefore, the correct option is Option 4.