copy array of char to another without strcpy in c

Your problem is that you are using only a single 'index' variable (i) for both source and destination strings. However, you should only increment the destination index if you actually copy a character. As it stands, when the source character is not copied, you are still incrementing the destination index, so you are skipping characters in that buffer, which are left in their original (i.e. uninitialized/garbage) states.

You need a separate index (let's call it j) for your destination buffer; initialize that to zero (as with i) at the start of the for loop but only increment it if we actually copy something (this can be done best using the post-increment operator inside the [...] for the destination:

#include <iostream>
using namespace std;

int main()
{
    int i, j; // Need 2 index vars: one for source, one for destination
    char x[50], y[50];
    cout << "Enter : ";
    scanf_s("%[^\n]", x, static_cast<int>(sizeof(x))); // Note last argument is "int"
    for (i = j = 0; x[i] != '\0'; i++) // Set "j" to zero at loop start ...
        if ((x[i] >= 'a' && x[i] <= 'z') || (x[i] >= 'A' && x[i] <= 'Z')) {
            y[j++] = x[i]; // ...but only increment it on copy!
        }
    y[j] = '\0'; // Use Last "j" for position of nul terminator
    cout << y;
    return 0;
}

Here is another solution. More C++-ish than working with raw arrays and indices, while being not as high level as using std::ranges::remove_copy_if:

#include <cctype>
#include <iostream>
#include <string>

int main()
{
    std::cout << "Enter : ";
    std::string x;
    std::getline(std::cin, x);

    std::string y;
    for ((unsigned char const e : x)
        if (std::isalpha(e))
            y.push_back(e);

    std::cout << y << '\n';
}

Additional credits: HolyBlackCat and Adrian Mole.

Seems your excercise is more 'C' but the solution would look something like this since you require not to use (which is not recommended for production code) :

int main()
{
    const size_t buf_size = 64;
    const char* input = "car a car";
    char output[buf_size];

    const char* input_ptr = &input[0];
    const char* output_ptr_end = &output[buf_size - 2]; // leave room for one extra trailing 0
    char* output_ptr = &output[0];

    while ((*input_ptr != 0) && (output_ptr < output_ptr_end))
    {
        if (*input_ptr == ' ') input_ptr++; // skip space
        *output_ptr++ = *input_ptr++;
    }
    *output_ptr = 0;
}

copy array of char to another without strcpy in c++

You can for example use std::ranges::copy.

without space

You can use std::ranges::remove_copy_if. Example:

auto is_space = [](char c) {
    return c == ' ';
};
std::ranges::remove_copy_if(x, y, is_space);

char input[32];  // obtained text
char output[32];

char*in_pos     =   input;
char*out_pos    =   output;

for(char cur_char; (cur_char=*in_pos++); ) // while NULL not encountered
{
    if(
        (cur_char>='A'&&cur_char<='Z')|| // uppercase
        (cur_char>='a'&&cur_char<='z')|| // lowercase
        (cur_char>='0'&&cur_char<='9')   // digits
    )
        *out_pos++  =   cur_char; // output cur_char
}

*out_pos = 0; // NULL termination