FIR filter design and implementation meaning What is the output of the convolution meaning which is used in the FIR filter?

how can conclude the output of the FIR filter in the output according to the input $x[n]$?
I don't fully understand how you are expressing your question in English, so please accept my attempt.

Discrete convolution is 
$$ y[n]=\sum_{k=-\infty}^{\infty} x[n-k] h[k]
$$
where $y[n]$ is the output at time index $n$ and $h[k]$ is the impulse response.  The index $k$ ranges over $-\infty$ to $\infty$ if $h[n]$ is an infinite impulse response.

A causal convolution, i.e. the filter can only have output $y[n]$ for $x[n]$ ,$x[n-1]$ ,$x[n-2]$ $\dots$ $x[n-\infty]$ 
$$ y[n]=\sum_{k=0}^{\infty} x[n-k] h[k]
$$
if $h[0]\ne 0$, $h[1]\ne 0$, $h[2] \ne 0$, $\dots$ $h[N-1]\ne 0$ , $h[N]=0$,  $h[N+1]=0$, $\dots$,  $h[\infty]=0$, is of finite length, it is a FIR filter and


  what is the output of the convolution meaning which is used in the FIR
  filter ?


$$ y[n]=\sum_{k=0}^{N-1} x[n-k] h[k]
$$


  how can conclude the output of the FIR filter in the output according
  to the input x[n]?


$y[n]$ depends on a finite sum of $x[n]$  .  A FIR filter also need not necessarily be causal, but it doesn't change that $y[n]$ only depends on a finite sum of $x[n]$ 

I don't understand how design has anything to do with your question.