Q:

Add specific given numbers to get given result or as close as possible to such result

I'll explain by example; say my target result is the number 370.
and the numbers I can add together are 60, 64, 200, and 226. No other numbers.
What combination of these given numbers, when added together, gives me the desire result or as close as possible to the desire result. (We can repeat numbers).
one answer would be: 226 + 64 + 60 = 350, which is close to 370 (by 20 units).
but a better answer is: 200 + 64 + 64 + 60 = 388, which is closer to 370 (by 18 units).
The numbers above are just an example, I just don't know how to better explain the question but by giving an example.

A:

Let's say your target number is $N$ and the numbers you can use are : $a_0 , a_1 , a_2 .....,a_k $.
Hence , according to your question , :
$$a_oi_0 + a_1i_1 + a_2i_2 +......+a_ki_k = N \space\space\space\space\space\space \text{for some } (i_o,i_1,i_2....i_n \in \mathbb Z)$$
It is pretty clear that it is not always possible to get to $N$. Also there are no hard rules to determine the terms $(i_o,i_1,i_2....i_n)$ as it clearly depends upon $N$ and the numbers allowed to use.
Since we have lot of variables and very little constraint , The best to find the combinations would be by a simple trial and error.
PS : If you assume  $(a_0 , a_1 , a_2 .....,a_k )$ to be co-primes , then the question might take the form of  Chicken McNugget Theorem (or Postage Stamp Problem or Frobenius Coin Problem).
https://en.wikipedia.org/wiki/Postage_stamp_problem

