Need to put where the resource is coming from.
<TextBox Style="{StaticResource textStyleTextBox}"/>
Then define the style in a resource such as the user control resources:
<UserControl.Resources>
<Style TargetType="TextBox" x:Key="textStyleTextBox">
<Setter Property="Background" Value="Blue"/>
</Style>
</UserControl.Resources>
However I dont believe you want to set the style of the adornedelement within the placeholder. It's just a placeholder for any control with that template. You should set the style of the adornedelement in the element itself like the example I provided above. If you want to style the control based upon it's validation then something like this:
<Window.Resources>
<ControlTemplate x:Key="validationTemplate">
<DockPanel>
<TextBlock Foreground="Yellow" Width="55"
FontSize="18">!</TextBlock>
<AdornedElementPlaceholder/>
</DockPanel>
</ControlTemplate>
<Style x:Key="textBoxInError" TargetType="{x:Type TextBox}">
<Style.Triggers>
<Trigger Property="Validation.HasError" Value="true">
<Setter Property="Background" Value="Red"/>
<Setter Property="Foreground" Value="White"/>
</Trigger>
</Style.Triggers>
</Style>
</Window.Resources>
<StackPanel x:Name="mainPanel">
<TextBlock>Age:</TextBlock>
<TextBox x:Name="txtAge"
Validation.ErrorTemplate="{DynamicResource validationTemplate}"
Style="{StaticResource textBoxInError}">
<Binding Path="Age"
UpdateSourceTrigger="PropertyChanged" >
<Binding.ValidationRules>
<ExceptionValidationRule/>
</Binding.ValidationRules>
</Binding>
</TextBox>
</StackPanel>