Operator overloading ==, !=, Equals

I think you declared the Equals method like this:

public override bool Equals(BOX obj)

Since the object.Equals method takes an object, there is no method to override with this signature. You have to override it like this:

public override bool Equals(object obj)

If you want type-safe Equals, you can implement IEquatable<BOX>.

As Selman22 said, you are overriding the default object.Equals method, which accepts an object obj and not a safe compile time type.

In order for that to happen, make your type implement IEquatable<Box>:

public class Box : IEquatable<Box>
{
    double height, length, breadth;

    public static bool operator ==(Box obj1, Box obj2)
    {
        if (ReferenceEquals(obj1, obj2)) 
            return true;
        if (ReferenceEquals(obj1, null)) 
            return false;
        if (ReferenceEquals(obj2, null))
            return false;
        return obj1.Equals(obj2);
    }
    public static bool operator !=(Box obj1, Box obj2) => !(obj1 == obj2);
    public bool Equals(Box other)
    {
        if (ReferenceEquals(other, null))
            return false;
        if (ReferenceEquals(this, other))
            return true;
        return height.Equals(other.height) 
               && length.Equals(other.length) 
               && breadth.Equals(other.breadth);
    }
    public override bool Equals(object obj) => Equals(obj as Box);

    public override int GetHashCode()
    {
        unchecked
        {
            int hashCode = height.GetHashCode();
            hashCode = (hashCode * 397) ^ length.GetHashCode();
            hashCode = (hashCode * 397) ^ breadth.GetHashCode();
            return hashCode;
        }
    }
}

Another thing to note is that you are making a floating point comparison using the equality operator and you might experience a loss of precision.