For saving the history inside of one program run, an array is enough. For saving the history over multiple program runs (over closing by typing and invalid character or ctrl+c and restarting it), you would need to store it in a file.

You can already print the last conversion by reading the value of f_value/c_value without writing to it (note that if no conversion of that type has happened before, you will get garbage, and that you will have to modify the if at the start of the loop to check for ‘x’ too):

		if (choice == 'x') {  // x is the letter left of c, so i chose it as an easy example
			// we want to print the previous conversion, so we don't want to read in a new value.
			// printf("\nEnter the temperature in Celcius: ");  
			// scanf("%d", &c_value);  
			// you might need to comment this getchar() back in so your program skips over the enter after the x, but i am not sure.
			// getchar();  
			// no modification of the following line is needed, as the c_value of the last celcius conversion was never written too and as such still exists.
			printf("\n%d degrees Celcius is %.1f degrees Fahrenheit.\n", c_value, toFahrenheit(c_value));  
		}  

For a longer history you need some extra places to store the numbers. if you use an array, you need to store the length of the history too, since c does not store how far into the array you have written.

// at the start of your main function, where you also declare the other variables
	// allocate the array with fixed length
	int last_c_values[16];
	// and store how many values you've written to it. Initialize it to zero so you don't do garbage with it later on.
	int last_c_values_count = 0;

// after printing the conversion from celsius to farenheit
			if (last_c_values_count < 16) // we can't handle a history longer than that yet
				// copy over the current value into the array, the first one will be at index 0
				last_c_values[last_c_values_count] = c_value;
				// increase the counter so the next value will be at the next place
				last_c_values_count = last_c_values_count + 1;
				// or shorter: last_c_values_count++;
			}

//and the new choice for printing the stuff
		if (choice == 'x') {  // x is the letter left of c, so i chose it as an easy example
			// start at 0, as long as i is below last_c_values_count, increment i by one at the end of each loop run
			for (int i = 0; i < last_c_values_count; i++) {
				// copy the value from last_c_values at index i into c_value
				c_value = last_c_values[i]; 
				// and do the same calculation as before again.
				printf("\n%d degrees Celcius is %.1f degrees Fahrenheit.\n", c_value, toFahrenheit(c_value));  
			}
		}

PS: the for loop in here is equivalent to the following while loop:

			int i = 0;
			while (i < last_c_values_count) {
				// copy the value from last_c_values at index i into c_value
				c_value = last_c_values[i]; 
				// and do the same calculation as before again.
				printf("\n%d degrees Celcius is %.1f degrees Fahrenheit.\n", c_value, toFahrenheit(c_value));  
				i++;
			}

you can absolutely save history in an array, but depending on how you want to do it, it can get very complex for a beginner.

the absolutely easiest way to go about it with how you’ve structured the program so far is making global arrays of just numbers, one for C->F conversions and one for the other way round. you also need to keep track of where in each array you are so you don’t go out of bounds. this requires minimal changes.

float c_to_f[5] ={0,0,0,0,0};
int c_to_f_length = 5;
int c_to_f_index = 0;

and update your input handler:

scanf("%d", &c_value);
c_to_f[c_to_f_index] = c_value;
c_to_f_index++;
if (c_to_f_index >= c_to_f_length) c_to_f_index = 0;

and then when you want to see the list results, you do

for (int i = 0; i < c_to_f_length; i++) {
    printf("%d\n", c_to_f[i];
}

this will of course not be in order of insertion, and if you want to show more than just the numbers you need to do some tinkering.

this is however a great jumping-off point to talk about many different concepts:

• do you feel like you’re just writing the same thing over and over? look into encapsulation and refactoring your program to minimise repetition.
• do you want to store more information about each entry? time to learn about structs.
• do you want to store as many entries as you want, without having to specify? go learn about linked lists.
• do you want to be able to step back and forward through your history? check out the readline library, and learn how to do imports generally.

sorry if my formatting is off, i did this on my phone…