There are two main errors in your code, and a couple of other minor points.
First, you can't directly assign arrays (be they character strings or any other array type) in C; for nul-terminated char arrays (strings), you can copy one to another using the strcpy function, or copy part of one to another using strncpy (which is what you want in your case).
Second, you can't print a string using the %c format specifier – you need %s for those.
And, a less serious issue (but one to avoid, if you want to be a good programmer) is that functions that work with string lengths (like strlen and strncpy) generally use size_t types, rather than int; and these require using the %zu format specifier, in place of %d.
Here's a version of your code that does what you want:
#include <stdio.h>
#include<string.h>
#define DIM 99
int main()
{
char name[DIM], name2[DIM] = { 0 }; // Fill with zeros to start, so we will have a nul terminator
size_t length, length2; // Strictly, use "size_t" for "strlen" and "strncpy"
printf("Enter a word: ");
scanf("%s", name);
length = strlen(name);
printf("The word's length is: %zu\n", length); // Use "%zu" for the "size_t" type
printf("Enter a smaller number than the length: ");
scanf("%zu", &length2); //Again, "%zu" for "size_t"
strncpy(name2, name, length2); // Use this function to copy a substring!
printf("The word cut on the letter %zu is: %s", length2, name2);// Note that you need "%s" to print a string
return 0;
}
There are some other 'safety measures' that you can add to your code, to prevent buffer overruns and other faults. One would be to limit the initial string input to at most DIM - 1 characters; this would be trivial if you had a hard-coded value of 99 in place of DIM, because then you could use a call like the following:
scanf("%98s", name); // Read at most 98 characters (leaving space for the nul-terminator)
However, the macro DIM cannot be used inside the quoted format string. Instead, you can write its value (minus 1) into a separate string and use that as the format argument to scanf; so, we replace our initial scanf call, like so:
// scanf("%s", name); // This has the potential to overrun the "name" array!
char fmt[8];
sprintf(fmt, "%%%ds", DIM - 1); // Write "%98s" into the "fmt" string ...
scanf(fmt, name); // ...and use that for the "scanf" format
(Note that some compilers will warn about not using a string literal for the format argument, and some programmers may not 'approve' of doing so; however, it is perfectly legal C and, IMHO, a valid use of the scanf function.)