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Here I need to give the systematic name of this molecule so I decided to first find the longuest chain of carbons which seems to be the one I put in red. Then I have 2 ethyls at 3 and 4 and I have an isobutyl at 6 so would the name be

3,4-diethyl-6-isobutyldecane ?

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The name ‘3,4-diethyl-6-isobutyldecane’ that is proposed in the question is unambiguous and describes the correct structure. However, it corresponds to obsolete IUPAC recommendations.

The retained prefix ‘isobutyl’ was still contained in the 1993 recommendations but is explicitly no longer recommended in the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book).

According to current IUPAC recommendations, the preferred prefix for the group $\ce{(CH3)2CH-CH2-{}}$ is ‘2-methylpropyl’.

Therefore, the preferred IUPAC name (PIN) for the compound given in the question is 3,4-diethyl-6-(2-methylpropyl)decane.

3,4-diethyl-6-(2-methylpropyl)decane

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Isobuytl is a trivial name (Although it is very clear what is means, even if not formally correct).

Try:

3,4-diethyl-6-(2-methylpropyl)-decane

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