Cannot implicitly convert type 'string' to 'System.Threading.Tasks.Task<string>'

The listed return type of the method is Task<string>. You're trying to return a string. They are not the same, nor is there an implicit conversion from string to Task<string>, hence the error.

You're likely confusing this with an async method in which the return value is automatically wrapped in a Task by the compiler. Currently that method is not an async method. You almost certainly meant to do this:

private async Task<string> methodAsync() 
{
    await Task.Delay(10000);
    return "Hello";
}

There are two key changes. First, the method is marked as async, which means the return type is wrapped in a Task, making the method compile. Next, we don't want to do a blocking wait. As a general rule, when using the await model always avoid blocking waits when you can. Task.Delay is a task that will be completed after the specified number of milliseconds. By await-ing that task we are effectively performing a non-blocking wait for that time (in actuality the remainder of the method is a continuation of that task).

If you prefer a 4.0 way of doing it, without using await , you can do this:

private Task<string> methodAsync() 
{
    return Task.Delay(10000)
        .ContinueWith(t => "Hello");
}

The first version will compile down to something that is more or less like this, but it will have some extra boilerplate code in their for supporting error handling and other functionality of await we aren't leveraging here.

If your Thread.Sleep(10000) is really meant to just be a placeholder for some long running method, as opposed to just a way of waiting for a while, then you'll need to ensure that the work is done in another thread, instead of the current context. The easiest way of doing that is through Task.Run:

private Task<string> methodAsync() 
{
    return Task.Run(()=>
        {
            SomeLongRunningMethod();
            return "Hello";
        });
}

Or more likely:

private Task<string> methodAsync() 
{
    return Task.Run(()=>
        {
            return SomeLongRunningMethodThatReturnsAString();
        });
}

Use FromResult Method

public async Task<string> GetString()
{
   System.Threading.Thread.Sleep(5000);
   return await Task.FromResult("Hello");
}

Beyond the problematic use of async as pointed out by @Servy, the other issue is that you need to explicitly get T from Task<T> by calling Task.Result. Note that the Result property will block async code, and should be used carefully.

Try:

private async void button1_Click(object sender, EventArgs e)
{
    var s = await methodAsync();
    MessageBox.Show(s.Result);
}