How do I change the following C# code from using a while loop to for loop?

You are declareign x twice, once here:

int x = 1;

And once here:

for(int x = 1;i<=10;i++)

That's not a good idea as the compiler will tell you:

A local variable named 'x' cannot be declared in this scope because it would give a different meaning to 'x', which is already used in a 'parent or current' scope to denote something else

And you don't declare i at all!
Then there is the ending condition, which isn't the same for the two loops - your new one would perform an extra iteration because it continues to run even when i is equal to 10.
To change this

int x = 1;
while (x < 10)
    {
    Console.Write(x);
    x++;
    }

to a for loop, just do this:

for (int x = 1; x < 10; x++)
    {
    Console.Write(x);
    }

In the "for" you are setting x to 1, then checking if i is <= 10, then incrementing i.

int x = 1;
for(int x = 1;i<=10;i++)
{
Console.Write(x);
x++;
}

Change to

int x = 1;
for(int i = 1;i<=10;i++)
{
Console.Write(x);
x++;
}

Or you could get rid of x altogether

for(int i = 1;i<=10;i++)
{
Console.Write(i);
}

for(int i = 1; i < 10; i++)
{
   Console.Write(i);
}