Not sure how you're creating the forms, but let's say that the main form is created first and the independent form is created from the main form. So, in your independent form declaration, pass in the main form so that you can access it's properties
IndependentForm form2 = New IndependentForm(this);
form2.Show();
The IndependentForm would look like
public partial class IndependentForm : Form
{
MainForm _parent;
Boolean _pictureBoxVisble;
public IndependentForm(MainForm parent)
{
_parent = parent;
_pictureBoxVisible = false;
}
public void Button1_Click(object sender, EventArgs e)
{
_pictureBoxVisble = !_pictureBoxVisible;
_parent.SetPictureBoxVisible(_pictureBoxVisible);
}
}
Then, when you click the button on the independent form, you have the reference to the initial form and you can call a property or function on the main form.
mainForm.SetPictureBoxVisible(TrueOrFalseValue);