lol

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We should be going out on date for all this hard work i did xP

Here's how you can approach the problem:

1. Write the Congruence:
   The given congruence is 7x + 3 ≡ 2x - 4(mod 16).

2. Combine Like Terms:
   Combine the x terms and constants on both sides of the congruence:
   5x + 3 ≡ -4(mod 16)

3. Use the Modular Inverse:
   Multiply both sides by the modular inverse of 5 modulo 16, which is 13 in this case:
   13(5x + 3) ≡ 13(-4)(mod 16)

4. Simplify:
   Simplify both sides of the congruence:
   65x + 39 ≡ -52 (mod 16)

5. Reduce Coefficients:
   Reduce the coefficients on both sides modulo 16:
   1x + 7 ≡ 4 (mod 16)

6. Solve for x:
   Subtract 7 from both sides:
   1x ≡ -3 (mod 16)

7. Check the Solution:
   Check if your solution satisfies the original congruence: (7x + 3 ≡ 2x - 4 (mod 16).

So, the solution to the congruence is x ≡ -3 (mod 16). 
You can also express this as x ≡ 13 (mod 16) since -3 is congruent to 13 modulo 16.

Remember that in modular arithmetic, adding or subtracting multiples of the modulus doesn't change the congruence, so adding or subtracting 16 from the solution won't affect its validity.