Hi all,
I have constructed a gene tree using 27 genes using the Maximum likelihood method with MEGA X. However, even though the bootstrap values on the branches look good, the likelihood value given by MEGA for that tree is -9745.782. I don't understand. Please help.

For many applications, the natural logarithm of the likelihood
function, called the log-likelihood, is more convenient to work with.
This is because we are generally interested in where the likelihood
reaches its maximum value: the logarithm is a strictly increasing
function, so the logarithm of a function achieves its maximum value at
the same points as the function itself, and hence the log-likelihood
can be used in place of the likelihood in maximum likelihood
estimation and related techniques. Finding the maximum of a function
often involves taking the derivative of a function and solving for the
parameter being maximized, and this is often easier when the function
being maximized is a log-likelihood rather than the original
likelihood function, because the probability of the conjunction of
several independent variables is the product of probabilities of the
variables and solving an additive equation is usually easier than a
multiplicative one.

As a by product of likelihoods values being really tiny (close to zero), log-likelihood values are negative.

Absolute likelihood values do not say if the recovered tree is good or not, but, when estimating trees with the same dataset using different substitution models, likelihood values can help choosing the best tree.

Does the following post helps?

I am wondering why we use negative (log) likelihood sometimes?

Yes it does help a bit. Based on that link, I gather that it is commonplace to have negative log likelihood values for phylogenetic trees?