Make masterpage for default.aspx to ThreeColumn.master
if you did that already then go to admin section > Configuration > Global Settings > Choose last tab "Other" and find this:
Show mini-shopping cart: CHECK MARK and SAVE CHANGES
now you will be able to see mini shopping cart on your homepage
In order to make mini-shopping cart's position to the left go to ThreeColumn.master page
Inside this section:
<div class="master-wrapper-rightside-3">
<asp:ContentPlaceHolder ID="cph3" runat="server">
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.......
you will see this:
<nopCommerce:MiniShoppingCartBox ID="ctrlMiniShoppingCartBox" runat="server" />
cut it from there and paste it above inside this section:
<div class="master-wrapper-leftside-3">
<asp:ContentPlaceHolder ID="cph2" runat="server">
....
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