WPF Listbox Show Button in ItemTemplate on MouseOver

Question

Ok, try this in your button declaration:

<Button x:Name="sideButton" Width="20">
    <Button.Style>
        <Style TargetType="{x:Type Button}">
            <Setter Property="Visibility" Value="Hidden" />
            <Style.Triggers>
                <DataTrigger Binding="{Binding RelativeSource={RelativeSource Mode=FindAncestor,AncestorType={x:Type ListBoxItem}},Path=IsMouseOver}" Value="True">
                    <Setter Property="Visibility" Value="Visible" />
                </DataTrigger>
            </Style.Triggers>
        </Style>
    </Button.Style>
</Button>

So I'm using a style with a trigger to look back up the visual tree until I find a ListBoxItem, and when its IsMouseOver property flips over to True I set the button's visibility to Visible.

See if it's close to what you want.

This Style does what you need. On mouse over, the button becomes only visible when the pointer is over the ListBoxItem. The special trick is to bind to the TemplatedParent for reaching IsMouseOver and use TargetName on the Setter to only affect the Button.

<Style TargetType="{x:Type ListBoxItem}">
    <Setter Property="ContentTemplate">
        <Setter.Value>
            <DataTemplate>
                <Border BorderBrush="Black"
                        BorderThickness="1"
                        Margin="6">
                    <StackPanel Orientation="Horizontal">
                        <Image Source="{Binding Path=FullPath}"
                               Height="150"
                               Width="150" />
                        <Button x:Name="sideButton"
                                Width="20"
                                Visibility="Hidden" />
                    </StackPanel>
                </Border>
                <DataTemplate.Triggers>
                    <DataTrigger Binding="{Binding IsMouseOver,RelativeSource={RelativeSource TemplatedParent}}"
                                 Value="True">
                        <Setter Property="Visibility"
                                TargetName="sideButton"
                                Value="Visible" />
                    </DataTrigger>
                </DataTemplate.Triggers>
            </DataTemplate>
        </Setter.Value>
    </Setter>
</Style>

@David is showing the right way, But I have one suggestion to your XAML architecture. If you don't have any DataBinding on the Button it is better to put that in to the ListBoxItem style than the DataTemplate as bellow.

  <Style TargetType="{x:Type ListBoxItem}">
        <Setter Property="ContentTemplate">
            <Setter.Value>
                <DataTemplate>
                    <Border BorderBrush="Black"
                    BorderThickness="1"
                    Margin="6">
                        <StackPanel Orientation="Horizontal">
                            <Image Source="{Binding Path=FullPath}"
                           Height="150"
                           Width="150" />                             
                        </StackPanel>
                    </Border>
                </DataTemplate>
            </Setter.Value>
        </Setter>            
        <Setter Property="Template">
            <Setter.Value>
                <ControlTemplate TargetType="{x:Type ListBoxItem}">
                    <Grid Background="Transparent">
                        <Button x:Name="sideButton" Width="20" HorizontalAlignment="Right" Visibility="Hidden" />
                        <ContentPresenter/>                            
                    </Grid>
                    <ControlTemplate.Triggers>
                        <Trigger  Property="IsMouseOver" Value="True">
                            <Setter Property="Visibility"
                            TargetName="sideButton"
                            Value="Visible" />
                        </Trigger>
                    </ControlTemplate.Triggers>
                </ControlTemplate>
            </Setter.Value>
        </Setter>            
    </Style>