Message decipher

Solution in Ruby. Created a hash with keys corresponding to '((i * 7) + 2) mod 26' (the encrypted character) and values corresponding to i (the original alphabetic character).

letters = {}

for i in (1..26)
  letters[((i * 7) + 2) % 26] = i # 0 equals to z here.
end

cipher = [6,11,8,8,3,7,3,24,8,4] # numeric positions for the FKHHCGCXHD letters.

message = []

cipher.each { |l| message.push(letters[l]) }

# message == [8, 5, 12, 12, 15, 23, 15, 18, 12, 4] : HELLOWORLD

s = 0

message.each { |n| s += n }

# s == 124

Simple algorithm in c++

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int main() {
    char txt[] = "fkhhcgcxhd"; //the input code
    int sum = 0;
    for(int i = 0; i < 10; i++) {
        int d = txt[i] - 'a' + 1; // get the value of the letter
        //(i.e.): f - 'a' + 1 = 6 + 1 = 7. F = 7
        for(int j = 1; j <= 26; j++) {
            if(((7 * j) + 2) % 26 == d) { // find the original letter
                sum += j; // add to sum
                break; // go to next letter if already found
            }
        }
    }
    cout << "Sum is: " << sum << endl;
}

Sum is $\boxed{124}$ .

First of all, the easy way is to list out all the transforms,

$\begin{array}{|c|c||c|c|} \text{Original Letter} & \text{Original Number x} & 7x+2 \pmod{26} & \text{Final Letter} \\ \hline A& 1& 9 & I\\ \hline\\ B&2& 16&P\\ \hline\\ C&3& 23&W\\ \hline\\ D&4& 4&D\\ \hline\\ E&5& 11&K\\ \hline\\ F&6& 18&R\\ \hline\\ G&7& 25&Y\\ \hline\\ H&8& 6&F\\ \hline\\ I&9&13&M\\ \hline\\ J&10& 20&T\\ \hline\\ K&11&1&A\\ \hline\\ L&12& 8&H\\ \hline\\ M&13& 15&O\\ \hline\\ N&14& 22&V\\ \hline\\ O&15& 3&C\\ \hline\\ P&16& 10&J\\ \hline\\ Q&17& 17&Q\\ \hline\\ R&18& 24&X\\ \hline\\ S&19& 5&E\\ \hline\\ T&20& 12&L\\ \hline\\ U&21& 19&S\\ \hline\\ V&22& 0&Z\\ \hline\\ W&23& 7&G\\ \hline\\ X&24& 14&N\\ \hline\\ Y&25& 21&U\\ \hline\\ Z&26& 2&B\\ \end{array}$

Thus, the code "FKHHCGCXHD" is actually "HELLOWORLD" and has it's sum as $8+5+12+12+15+23+15+18+12+4= \boxed{124}$